Preprints in general harmonic analysis

Math 254A home page - oscillatory integrals, Diagonal entries of matrices, Scattering for Schrodinger with potential (1999)

Papers, and projects close to completion





On the almost-everywhere convergence of wavelet summation methods


ACHA 3 (1996), 384-387

dvi Plain TeX

Harmonic convolution operators on Lipschitz graphs


Adv. Appl. Clifford Alg. 6 (1996), 207-218

dvi Plain TeX

Almost everywhere convergence of general wavelet shrinkage estimators

Brani Vidakovic

ACHA 9 (2000), 72-82


The weak-type (1,1) of L \log L homogeneous convolution operators


Indiana U. Math. J. 48 (1999), 1547-1584

dvi + Figures1234

Convex bodies with a point of curvature do not admit exponential bases

Alex Iosevich 
Nets Katz

Amer. J. Math. 123 (2001), 115-120


Endpoint multiplier theorems of Marcinkiewicz type

Jim Wright

Revista Mat. Iber. 17 (2001), 521-558


Sharp Lorentz space estimates for rough operators

Andreas Seeger

Math. Annalen 320 (2001) 2, 381-415


L^p improving estimates for averages along curves

Jim Wright

J. Amer. Math. Soc. 16 (2003), 605-638

Short slides 
dvi +Fig. 1 
Long slides 

A converse extrapolation theorem for translation-invariant operators


J. Funct. Anal. 180 (2001), 1-10


The Fuglede spectral conjecture holds for convex bodies in the plane

Alex Iosevich 
Nets Katz

Math. Res. Letters 10 (2003), 559-570


Some light on Littlewood-Paley theory

Michael Cowling

Math. Annalen 321 (2001) 4, 885-888


Endpoint mapping properties of spherical maximal operators

Andreas Seeger 
Jim Wright

J. Institut Math. Jussieu 2 (2003) 1, 109-144


Pointwise convergence of lacunary spherical means

Andreas Seeger 
Jim Wright

Mt. Holyoke Proceedings (2001), Contemporary Mathematics (2003), 341-352


Singular maximal functions and Radon transforms near L^1

Andreas Seeger 
Jim Wright

Amer. J. Math. 126 (2004), 607-647.


Carleson measures, trees, extrapolation, and T(b) theorems

Pascal Auscher 
Steve Hofman 
Camil Muscalu 
Christoph Thiele

Publications Matematiques Barcelona 46 (2002), 257-325

Expository version

Weak-type (1,1) bounds for Fourier integral operators


J. Aust. Math. Soc. 75 (2003), 1-21.


Fuglede's conjecture is false in 5 and higher dimensions


Math. Res. Letters 11 (2004), 251-258


An uncertainty principle for cyclic groups of prime order


Math. Res. Letters 12 (2005), 121-127


The Brascamp--Lieb Inequalities: Finiteness, Structure and Extremals

Jon Bennett
Tony Carbery
Michael Christ

GAFA 17 (2008), 1343-1415


Finiteness bounds for Holder-Brascamp-Lieb multilinear inequalities

Jon Bennett
Tony Carbery
Michael Christ

Submitted,  Math. Res. Letters


A quantitative version of the Besicovitch projection theorem via multiscale analysis

Proc. Lond. Math. Soc. doi:10.112/plms/pdn037


Random Martingales and localization of maximal inequalities Assaf Naor Submitted, J. Funct. Anal. math.CA/0902.1140
Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem
Assaf Naor
Submitted, Israel J. Math.

Preprints specific to the Kakeya, Restriction, and Bochner-Riesz problems can be found here
Preprints specific to multilinear operators 
can be found here
Preprints specific to sparse recovery problems 
can be found here.

Short stories

These are generally very short, toy versions of real results due to other people, and are not publication-quality.  Caveat emptor.  All files other than figures are in dvi format.  Unlike the preprints, these articles are fluid and subject to new developments.  Please let me know if you have any comments, references, etc. on any of them.

Disclaimer: Many of the notes here are based on papers written by other people.  My intention here is not to try to "beat" these authors' work in any way, but rather to isolate the main ingredients of the argument, which are often very beautiful, and try to present them in as simple and brief a context as possible (often sacrificing generality, rigour, and/or details in order to do this).  Certainly I do not view these notes as worthy of publication in a refereed journal, and are definitely inferior to the original article in every single aspect, with the possible exception of brevity. 

Counterexample to a self-adjoint Hardy-Littlewood inequality

The weak-type (1,1) of the parabolic maximal function

Holder's inequality for Lorentz spaces

Dyadic product H^1, and Carleson's counterexample

Real interpolation of Lorentz spaces

Notes on Hausdorff and Minkowski dimension

Atomic decomposition of Orlicz spaces, and extrapolation

Spectral pairs and tiling

Summability of functions

A hasty interpolation

The dyadic pigeonhole principle in harmonic analysis

Going to extremes

A quantitative proof of Wiener's theorem

L^p non-invertibility of frame operators

Dyadic Journe's lemma

Abstract kernel manipulation

A Bellman function proof of the John-Nirenberg inequality

Tree chopping, and Carleson measures

The T(b) theorem and its variants

The non-linear Fourier transform

The weak-type (1,1) of the spherical maximal function

The Fourier transform on non-abelian finite groups

Technical survey of harmonic analysis

Symmetries, scaling, and dimensional analysis

The Christ cube construction

The Lindenstrauss maximal inequality

Wolff.s proof of the corona theorem

Ornstein.s counterexample to an L^1 maximal inequality

Uchiyama.s constructive proof of the Fefferman-Stein decomposition

Soft analysis, hard analysis, and the finite convergence principle

The Lebesgue differentiation theorem and the Szemeredi regularity lemma

Ultrafilters, nonstandard analysis, and epsilon management

Amplification, arbitrage, and the tensor power trick

Princeton Companion to Mathematics



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