Preprints and published papers

Most recent preprints can also be found in this list on arXiv .


Bochner-Riesz means at the critical index: Weighted and sparse bounds
With David Beltran and Joris Roos.
arXiv 2309.13487 , Oberwolfach Preprint OWP-2023-16

A note on endpoint Bochner-Riesz estimates
With David Beltran and Joris Roos.
Oberwolfach Preprint OWP-2023-17 .

Spherical maximal functions on two step nilpotent Lie groups
With Jaehyeon Ryu.
Advances in Mathematics, 453, September 2024, 109846.
arXiv 2309.07725

A sufficient condition for Haar multipliers on Triebel-Lizorkin spaces
With Gustavo Garrigós and Tino Ullrich.
arXiv 2301.11906

Endpoint sparse domination for classes of multiplier transformations
With David Beltran and Joris Roos.
Mathematische Zeitschrift, 305 no.1. (2023) article 11, 55 pages.
arXiv 2212.12437

Haar frame chacterizations of Besov-Sobolev spaces and optimal embeddings into their dyadic counterparts
With Gustavo Garrigós and Tino Ullrich.
Journal of Fourier Analysis and Applications, 29 (2023), no. 3, Paper No. 39.
arXiv 2209.02630

Spherical maximal operators on Heisenberg groups: Restricted dilation sets.
With Joris Roos and Rajula Srivastava.
Studia Mathematica, 273 (2023), no. 1, 1-28.
arXiv 2208.02774

Sobolev spaces revisited.
With Haïm Brezis, Jean Van Schaftingen and Po Lam Yung.
Rendiconti Lincei - Matematica e Applicazioni, 33 (2022), no.2, 413--437.
arXiv 2202.01410

Spaces of Besov-Sobolev type and a problem on nonlinear approximation.
With Óscar Domínguez, Brian Street, Jean Van Schaftingen and Po Lam Yung.
Journal of Functional Analysis, 284 (2023), no.4, 109775.
arXiv 2112.05539

Families of functionals representing Sobolev norms
With Haïm Brezis, Jean Van Schaftingen and Po Lam Yung
Analysis and PDE, 17-3 (2024), 943--979..
arXiv 2109.02930

Lebesgue space estimates for spherical maximal functions on Heisenberg groups
With Joris Roos and Rajula Srivastava.
International Mathematics Research Notices, IMRN 2022, no. 24, 19222--19257. Published online .
arXiv 2103.09734

Sobolev improving for averages over curves in R^4.
With David Beltran, Shaoming Guo and Jonathan Hickman.
Advances of Mathematics 393 (2021), Paper No. 108089. 85 p.
arXiv 2102.08806

Sharp L^p bounds for the helical maximal function.
With David Beltran, Shaoming Guo and Jonathan Hickman.
American Journal of Mathematics, to appear.
arXiv 2102.08272

Variation bounds for spherical averages.
With David Beltran, Richard Oberlin, Luz Roncal and Betsy Stovall.
Mathematische Annalen, 382 (2022), no.1-2, 459--512.
arXiv 2009.07366

Multi-scale sparse domination.
With David Beltran and Joris Roos.
Memoirs of the AMS, 298, Number 1491, June 2024.
arXiv 2009.00277
Offprint.

Spherical maximal functions and fractal dimensions of dilation sets.
With Joris Roos.
American Journal of Mathematics, 145, no. 4 (2023), 1077--1110.
arXiv:2004.00984

The circular maximal operator on Heisenberg radial functions.
With David Beltran, Shaoming Guo and Jonathan Hickman.
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5) 23 (2022), no.2, 501--568.
arXiv:1912.11718

L^p-L^q bounds for spherical maximal operators.
With Theresa C. Anderson, Kevin Hughes, and Joris Roos.
Mathematische Zeitschrift, 297 (2021), 1057-1074.
arXiv:1909.05389, Offprint

L^p-Sobolev estimates for a class of integral operators with folding canonical relations.
With Malabika Pramanik.
Journal of Geometric Analysis, 31 (2021), 6725-6765. DOI 10.1007/s12220-020-00388-0
arXiv:1909.04173, Offprint .

The Haar System in Triebel-Lizorkin spaces: Endpoint Results.
With Gustavo Garrigós and Tino Ullrich.
Journal of Geometric Analysis, 31 (2021), no.9, 9045--9089. DOI
arXiv:1907.03738

Basis properties of the Haar system in limiting Besov spaces..
With Gustavo Garrigós and Tino Ullrich.
Chapter in Geometric Aspects of Harmonic Analysis , 361-424.
Ed. by Paolo Ciatti and Alessio Martini. Springer INdAM Series, vol 45, 2021.
arXiv:1901.09117

Maximal functions associated with families of homogeneous curves: L^p bounds for p\le 2.
With Shaoming Guo, Joris Roos, and Po Lam Yung.
Proceedings of the Edinburgh Mathematical Society, 63, issue 2 (2020), 398--412.
arXiv:1906.05997

On pointwise convergence of Schrödinger means.
With Evangelos Dimou.
Mathematika, 66 (2020), 2, 356--372.
arXiv:1906.03727

A maximal function for families of Hilbert transforms along homogeneous curves .
With Shaoming Guo, Joris Roos, and Po Lam Yung.
Mathematische Annalen, Math. Ann. 377 (2020), no. 1-2, 69-114.
DOI , arXiv:1902.00096

Book review on
"Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra", by I.A. Ikromov and D. Müller.
Bulletin of the American Mathematical Society, 57, No.1 (2020), 145--151.
Offprint.

Riesz means of Fourier series and integrals: Strong summability at the critical index.
With Jongchon Kim.
Transactions of the American Mathematical Society, 372, No. 4 (2019), 2959-2999.
arXiv:1807.07854 Offprint.

Embeddings for spaces of Lorentz-Sobolev type.
With Walter Trebels.
First version.
Revision , July 2018.
arXiv:1801.10570
Mathematische Annalen, 373, No. 3-4 (2019), 1017--1056.

Spherical means on the Heisenberg group: Stability of a maximal estimate..
With Theresa C. Anderson, Laura Cladek, and Malabika Pramanik.
Journal d'Analyse Mathématique,145 (2021), no.1, 1-28.
arXiv:1801.06981

Multilinear singular integral forms of Christ-Journé type.
With Charles K. Smart and Brian Street.
Memoirs of the American Mathematical Society, vol. 257, No. 1231 (2019).
Offprint..

The Haar system as a Schauder basis in spaces of Hardy-Sobolev type.
With Gustavo Garrigós and Tino Ullrich.
Journal of Fourier Analysis and Applications, 24(5) (2018), 1319-1339.

Singular integrals and a problem on mixing flows.
With Mahir Hadžić, Charles Smart and Brian Street.
Annales de l'Institut Henri Poincare / Analyse non lineaire. 35, No. 4 (2018), 921--943.

On square functions with independent increments and Sobolev spaces on the line.
With Juliá Cufí, Artur Nicolau and Joan Verdera.
Annali di Matematica Pura ed Applicata (4) 197 (2018), no. 3, 905--940.

Lower bounds for Haar projections: Deterministic Examples.
With Tino Ullrich.
Constructive Approximation, 42, No.2. (2017), 227-242.

On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type.
With Gustavo Garrigós and Tino Ullrich.
Analysis Mathematica, 43, No. 2 (2017), 267--278.

Convolution powers of Salem measures with applications.
With Xianghong Chen.
Canadian Journal of Mathematics, 69, No.2 (2017), 284-320.

Haar projection numbers and failure of unconditional convergence in Sobolev spaces..
With Tino Ullrich.
Mathematische Zeitschrift, 285 (2017), 91-119.

Sharp L^p-bounds for the wave equation on groups of Heisenberg type.
With Detlef Müller.
Analysis and PDE, Vol. 8 (2015), No. 5, 1051-1100.

On radial Fourier multipliers and almost everywhere convergence.
With Sanghyuk Lee.
Journal of the London Mathematical Society, (2) 91 (2015), no. 1, 105--126.

A weak type bound for a singular integral.
Revista Matemática Iberoamericana, 30 (2014), no. 3, 961-978.

Square functions and maximal operators associated with radial Fourier multipliers.
With Sanghyuk Lee and Keith M. Rogers.
Chapter 12 in "Advances in Analysis: The Legacy of Elias M. Stein"
Princeton University Press, 2014.

Restriction of Fourier transforms to curves:
An endpoint estimate with affine arclength measure.
With Jong-Guk Bak and Daniel Oberlin.
Journal für die reine und angewandte Mathematik, 682 (2013), 167-206.

Lebesgue space estimates for a class of Fourier integral operators
associated with wave propagation.
With Sanghyuk Lee.
Mathematische Nachrichten, 286 (2013), 743-755. 978.

On space time estimates for the Schrödinger operator.
With Sanghyuk Lee and Keith M. Rogers.
Journal de Mathématiques Pures et Appliquées, 99, no.1 (2013), 62-85.
A correction.

Improved bounds for Stein's square functions,
with Sanghyuk Lee and Keith M. Rogers.
Proceedings of the London Mathematical Society, 104 (2012), 1198-1234.
pdf, revised version.

A variation norm Carleson theorem,
with Richard Oberlin, Terence Tao, Christoph Thiele and James Wright .
Journal of the European Mathematical Society, 14 (2012), 421--464.
arXiv:0910.1555, pdf.

Problems on averages and lacunary maximal functions,
with James Wright.
Józef Marcinkiewicz Centenary Volume.
Banach Center Publications, vol. 95 (2011), 235-250.
pdf.

Extensions of the Stein-Tomas theorem,
with Jong-Guk Bak.
Mathematical Research Letters, 18 (2011), 767--781.
pdf, reprint .

On radial and conical Fourier multipliers,
with Yaryong Heo and Fëdor Nazarov.
Journal of Geometric Analysis, 21 (2011) issue 1, 96-117.
pdf.

Radial Fourier multipliers in high dimensions,
with Yaryong Heo and Fëdor Nazarov.
Acta Mathematica, 206, No 1 (2011), 55-92.
pdf.
The earlier version with F. Nazarov (which
will remain unpublished) can be found here.

A Calderón-Zygmund estimate with applications
to generalized Radon transforms and Fourier integral operators,
with Malabika Pramanik and Keith M. Rogers.
Studia Mathematica, 202 (2011), 1-15.
pdf.

Endpoint maximal and smoothing estimates for Schrödinger equations.
with Keith Rogers.
Journal für die reine und angewandte Mathematik, 640 (2010), 47-66.
pdf.

A mixed norm variant of Wolff's inequality for paraboloids,
with Gustavo Garrigós.
In Harmonic Analysis and Partial Differential Equations, Contemporary Mathematics, vol. 505,
Amer. Math. Soc., Providence, RI, 2010, pp. 179-197.
pdf, 'offprint'.

A note on maximal operators associated with Hankel multipliers,
with Gustavo Garrigós.
Revista de la Unión Matemática Argentina, 50 No.2 (2009), 137-148.
pdf.

On plate decompositions of cone multipliers,
with Gustavo Garrigós.
Proceedings of the Edinburgh Mathematical Society, 52 (2009), 1-21.
pdf.
Earlier unpublished version in
Proceedings of the Harmonic Analysis and its Applications at Sapporo (2005)
Department of Mathematics, Hokkaido University Preprint server, Technical report 103 .
pdf.

Restriction of Fourier transforms to curves and related oscillatory integrals,
with Jong-Guk Bak and Daniel Oberlin.
American Journal of Mathematics, 131, no.2 (2009), 277-311.
pdf.

Low regularity classes and entropy numbers,
with Walter Trebels.
Archiv der Mathematik, 92, No. 2 (2009), 147-157.
pdf.

The Fourier extension operator on large spheres and related oscillatory integrals,
with Jonathan Bennett.
Proceedings of the London Mathematical Society, 98, no.1, (2009), 45-82.
pdf.

Restriction of Fourier transforms to curves,
II: Some classes with vanishing torsion,
with Jong-Guk Bak and Daniel Oberlin.
Journal of the Australian Mathematical Society, 85 (2008), 1-28.
pdf.

Characterizations of Hankel multipliers,
with Gustavo Garrigós.
Mathematische Annalen, 342, no. 1, Sept. 2008, 31-68.
pdf.

Strong variational and jump inequalities in harmonic analysis,
with Roger L. Jones and James Wright.
Transactions of the American Mathematical Society, 360 (2008), 6711-6742.
ps, pdf.

L^p regularity of averages over curves and bounds for associated maximal operators,
with Malabika Pramanik.
American Journal of Mathematics, 129, no.1 (2007), 61-103.
pdf .

Average decay estimates for Fourier transforms of measures supported on curves,
with Luca Brandolini, Giacomo Gigante, Allan Greenleaf, Alex Iosevich, Giancarlo Travaglini.
Journal of Geometric Analysis, 17, no 1 (2007), 15--40.
pdf.

Mean lattice point discrepancy bounds, II: Convex domains in the plane,
with Alexander Iosevich and Eric T. Sawyer.
ps (2004 files).
pdf, 2007 revised version, appeared in
Journal d'Analyse Mathématique, 101, No. 1 (2007), 25-63.

Necessary conditions for vector-valued operator inequalities in harmonic analysis,
with Michael Christ.
Proceedings of the London Mathematical Society, 93, 2 (2006), 447-473.
pdf.
File with later corrections: pdf.

L^p Sobolev regularity of a model restricted X-ray transform in R^3.
with Malabika Pramanik.
Proceedings of the conference on Harmonic Analysis and its Applications,
Osaka, November 2004,
pp. 47--64, Yokohama Publishers (2006).
pdf.

On maximal functions for Mikhlin-Hörmander multipliers,
with Loukas Grafakos and Petr Honzík.
Advances in Mathematics, 204 (2006), 363-378.
ps , pdf .

Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type,
with Michael Christ, Loukas Grafakos and Petr Honzík.
Mathematische Zeitschrift, 249 (2005), 223-240.
ps , pdf ..

Singular integral and maximal operators associated to hypersurfaces: L^p theory,
with Stephen Wainger, James Wright and Sarah Ziesler.
Journal of Geometric Analysis, 15, no. 3 (2005), 477-498.
pdf.

A family of singular oscillatory integral operators and failure of weak amenability,
with Michael Cowling, Brian Dorofaeff and James Wright.
Duke Mathematical Journal, 127, No.3 (2005), 429--486.
ps , pdf .

Singular spherical maximal operators on a class of step two nilpotent Lie groups,
with Detlef Müller.
Israel Journal of Mathematics, 141 (2004), 315--340.
ps , pdf .

Singular maximal functions and Radon transforms near L^1,
with Terence Tao and James Wright.
American Journal of Mathematics, 126 (2004), 607--647.
ps , pdf .
A correction. August 2005. pdf.

Pointwise convergence of lacunary spherical means,
with Terence Tao and James Wright.
Harmonic Analysis at Mount Holyoke,
Contemporary Mathematics 320, pp. 343-354, 2003
ps , pdf .

Endpoint mapping properties of spherical maximal operators,
with Terence Tao and James Wright.
Journal de l'Institut Mathématiques de Jussieu, 2 (2003), 109-144.
ps , pdf .

Singular Radon transforms and maximal functions under convexity assumptions,
with Stephen Wainger.
Revista Matemática Iberoamericana, 19 (2003), 1019-1044.
ps , pdf .

Bounds for singular fractional integrals and related Fourier integral operators,
with Stephen Wainger.
ps , pdf .
Preprint, September 2000, final version appears in Journal of Functional Analysis, 199 (2003), 48--91.

Oscillatory and Fourier integral operators with degenerate canonical relations,
with Allan Greenleaf.
Publicacions Matemàtiques (2002), 93-141.
Special issue: Proceedings of the El Escorial Conference 2000.
ps , pdf .

Mean square discrepancy bounds for the number of lattice points in large convex bodies,
with Alex Iosevich and Eric Sawyer.
Journal d'Analyse Mathématique, 87 (2002), 209--230.
ps , pdf .

Two endpoint bounds for generalized Radon transforms in the plane,
with Jong-Guk Bak and Daniel Oberlin.
Revista Matemática Iberoamericana, 18 (2002), 231-247.
ps , pdf .

Oscillatory integral operators with low-order degeneracies,
with Allan Greenleaf.
Duke Mathematical Journal, 112 (2002), 397--420.
ps , pdf .

Two problems associated with convex finite type domains,
with Alex Iosevich and Eric Sawyer.
Publicacions Matemàtiques, 46 (2002), 153-177.
ps , pdf .

Regularity properties of wave propagation on conic manifolds
and applications to spectral multipliers,
with Detlef Müller.
Advances in Mathematics, 161 (2001), 41--130.
ps , pdf .

Sharp Lorentz space estimates for rough operators,
with Terence Tao.
Mathematische Annalen 320 (2001), 381-415.
ps , pdf .

Estimates for generalized Radon transforms in three and four dimensions,
with Allan Greenleaf and Stephen Wainger.
Survey article, in:
Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis,
Contemporary Mathematics 251, AMS 2000, 243-254.
ps , pdf .

Riesz means associated with convex domains in the plane,
with Sarah Ziesler.
Mathematische Zeitschrift, 236 (2001), 643--676.
ps , pdf .

Weighted inequalities for Bochner-Riesz means in the plane,
with Anthony Carbery.
Quarterly Journal of Mathematics, 51 (2000), 155-169.
ps , pdf .

On averaging operators associated with convex hypersurfaces of finite type,
with Alexander Iosevich and Eric Sawyer.
Journal d'Analyse Mathématique, 79 (1999), 159--187.
ps , pdf .

Classes of singular integral operators along variable lines,
with Anthony Carbery, Stephen Wainger and James Wright.
Journal of Geometric Analysis, 9, no. 4 (1999), 583--605.
ps , pdf .

Classes of singular integrals along curves and surfaces,
with Stephen Wainger, James Wright and Sarah Ziesler.
Transactions Amer. Math. Soc. 351 (1999), 3757--3769.
ps , pdf .

On X-ray transforms for rigid line complexes and integrals over curves in R^4,
with Allan Greenleaf and Stephen Wainger.
Proceedings of the American Mathematical Society, 127 (1999), 3533-3545
ps , pdf .

On oscillatory integrals with folding canonical relations,
with Allan Greenleaf.
Studia Mathematica, 132 (1999), 125--139
ps , pdf .

Radon transforms and finite type conditions.
Journal of the American Mathematical Society, 11 (1998), 869-897
ps , pdf .

Fourier integral operators with cusp singularities,
with Allan Greenleaf.
American Journal of Mathematics, vol. 120 (1998), 1077-1119.
Copyright 1998, The Johns Hopkins University Press.
ps , pdf .

Spherical maximal operators on radial functions,
with Stephen . Wainger and James Wright.
Mathematische Nachrichten, 187 (1997), 95-105.
pdf.

Endpoint inequalities for Bochner-Riesz multipliers in the plane,
Pacific Mathematical Journal, 174 (1996), 543--553.
pdf.

Singular integral operators with rough convolution kernels,
Journal of the American Mathematical Society, 9 (1996), 95-105.
pdf.

A note on pointwise convergence of quasiradial Riesz means, with Y. Kim.
Acta Sci. Math. 62 (1996), 187--199.

Pointwise convergence of spherical means,
with Stephen Wainger and James Wright.
Math. Proc. Cambr. Phil. Soc., 118 (1995) 115--124.

Multiparameter Calderón-Zygmund theory and interpolation of analytic families,
with Anthony Carbery.
Acta Sci. Math. 60 (1995), 71--97.

Inequalities for spherically symmetric solutions of the wave equation,
with Detlef Müller.
Math. Z. 218 (1995), 417--426 .

Homogeneous Fourier multipliers of Marcinkiewicz type,
with Anthony Carbery.
Arkiv för Matematik, 33 (1995), 45--80.
pdf.
arXiv:math/9502236

L^2 estimates for a class of singular oscillatory integrals,
Mathematical Research Letters, 1 (1994), 65--73.

Fourier integral operators with fold singularities,
with Allan Greenleaf.
J. reine ang. Math., 455 (1994), 35--56.
pdf.

Degenerate Fourier integral operators in the plane,
Duke Math. J. 71 (1993), 685--745.

Averages over convex hypersurfaces,
with Alexander Nagel and Stephen Wainger.
Amer. J. Math., 115 (1993), 903--927.

Local smoothing of Fourier integral operators and Carleson-Sjölin estimates,
with Gerd Mockenhaupt and Christopher D. Sogge.
J. Amer. Math. Soc., 6 (1993), 65--131.

H^p and L^p variants of multiparameter Calderón-Zygmund-theory,
with Anthony Carbery.
Trans. Amer. Math. Soc., 334 (1992), 719--747.

Wave front sets, local smoothing and Bourgain's circular maximal theorem,
with Gerd Mockenhaupt and Christopher D. Sogge.
Annals of Math., 136 (1992), 207--218.

Endpoint estimates for multiplier transformations on compact manifolds,
Indiana Univ. Math. J., 40 (1991), 471--533.

Regularity properties of Fourier integral operators,
with Christopher D. Sogge and Elias M. Stein.
Annals of Math., 133 (1991), 231--251.

Remarks on singular convolution operators,
Studia Math. 97 (1990), 91--114.

Bounds for eigenfunctions of differential operators,
with Christopher D. Sogge.
Indiana Univ. Math. J., 38 (1989), 669--682.

Estimates near L^1 for Fourier multipliers and maximal functions,
Archiv Math. 53 (1989), 188--193.

On the boundedness of functions of (pseudo)-differential operators on compact manifolds,
with Christopher D. Sogge.
Duke Math. J. 59 (1989), 709--736.

A note on Triebel-Lizorkin spaces,
Proc. Semester on Approximation theory and Function spaces (Warsaw 1986),
Banach Center Publications 22, Warsaw, 1989.
http://eudml.org/doc/263479.

A limit case of the Hörmander multiplier theorem,
Monatshefte für Mathematik, 105 (1988), 151--160.

Conditionally convergent series of linear operators in L^p spaces and L^p estimates for pseudo-differential operators,
with Anthony Carbery.
Proc. London Math. Soc. 57 (1988), 481--510.

Some inequalities for singular convolution operators in L^p-spaces,
Trans. Amer. Math. Soc. 308 (1988), 259--272.
http://eudml.org/doc/219011.

Necessary conditions for quasiradial Fourier multipliers,
Tohoku Math. J. 39 (1986), 249--257.

On quasiradial Fourier multipliers and their maximal functions,
J. reine ang. Math. { 370} (1986), 61--73.

A note on absolute summability of Fourier integrals,
Colloquia Mathematica Societatis Janos Bolyai 49, Alfred Haar Memorial Conference 1985.

Some Fourier multiplier criteria for anisotropic H^p(R^n)-spaces,
with Walter Trebels.
Acta Sci. Math 48 (1985), 431--441.

Unpublished manuscripts

Notes on radial and quasiradial Fourier multipliers
Expository paper
pdf.


Improvements in Wolff's inequality for decompositions of cone multipliers
With Gustavo Garrigós and Wilhelm Schlag
pdf.

Many papers are also posted at the arXiv.org preprint server at this link.

Research papers after 1991 supported in part by grants from the National Science Foundation.