Preprints and published papers


On square functions with independent increments and Sobolev spaces on the line.
With Juliá Cufí, Artur Nicolau and Joan Verdera.
To appear in Annali di Matematica Pura ed Applicata
pdf.

Singular integrals and a problem on mixing flows.
With Mahir Hadžić, Charles Smart and Brian Street.
To appear in Annales de l'Institut Henri Poincare / Analyse non lineaire
pdf.

The Haar system as a Schauder basis in spaces of Hardy-Sobolev type.
With Gustavo Garrigós and Tino Ullrich.
pdf.

Multilinear singular integral forms of Christ-Journé type.
With Charles K. Smart and Brian Street.
Memoirs of the American Mathematical Society, to appear.
pdf.

Already in print:

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

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.
pdf.

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

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

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.
pdf.

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

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

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.
pdf.

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.
pdf.

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

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.
pdf, revised version.
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 .

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.
A correction (March 2014) 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 .
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 .

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 .

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 ,

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 .

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 .

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 .

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 .

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 .

On X-ray transforms for rigid line complexes and integrals over curves in R^4,
with Allan Greenleaf and Stephen Wainger.
Proc. Amer. Math. Soc. 127 (1999), 3533-3545
ps , pdf .

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

Radon transforms and finite type conditions.
Journal Amer. Math. Soc., 11 (1998), 869-897
ps .

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 .

Earlier papers.

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

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