Preprints in general harmonic analysis

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

Harmonic Analysis mailing list

Harmonic analysis links

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Papers, and projects close to completion

Title	With	Status	Download
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	ps
The weak-type (1,1) of L \log L homogeneous convolution operators		Indiana U. Math. J. 48 (1999), 1547-1584	math.CA/9903165 Slides: dvi + Figures 1234
Convex bodies with a point of curvature do not admit exponential bases	Alex Iosevich Nets Katz	Amer. J. Math. 123 (2001), 115-120	math.CA/9911167
Endpoint multiplier theorems of Marcinkiewicz type	Jim Wright	Revista Mat. Iber. 17 (2001), 521-558	math.CA/0001050
Sharp Lorentz space estimates for rough operators	Andreas Seeger	Math. Annalen 320 (2001) 2, 381-415	math.CA/9912098
L^p improving estimates for averages along curves	Jim Wright	J. Amer. Math. Soc. 16 (2003), 605-638	math.CA/0108137 Short slides dvi + Fig. 1 Long slides dvi
A converse extrapolation theorem for translation-invariant operators		J. Funct. Anal. 180 (2001), 1-10	math.FA/9912001
The Fuglede spectral conjecture holds for convex bodies in the plane	Alex Iosevich Nets Katz	Math. Res. Letters 10 (2003), 559-570	math.CA/0104087
Some light on Littlewood-Paley theory	Michael Cowling	Math. Annalen 321 (2001) 4, 885-888	math.CA/0011246
Endpoint mapping properties of spherical maximal operators	Andreas Seeger Jim Wright	J. Institut Math. Jussieu 2 (2003) 1, 109-144	math.CA/0205153
Pointwise convergence of lacunary spherical means	Andreas Seeger Jim Wright	Mt. Holyoke Proceedings (2001), Contemporary Mathematics (2003), 341-352	math.CA/0205154
Singular maximal functions and Radon transforms near L^1	Andreas Seeger Jim Wright	Amer. J. Math. 126 (2004), 607-647.	math.CA/0205156
Carleson measures, trees, extrapolation, and T(b) theorems	Pascal Auscher Steve Hofman Camil Muscalu Christoph Thiele	Publications Matematiques Barcelona 46 (2002), 257-325	math.CA/0108138 Expository version
Weak-type (1,1) bounds for Fourier integral operators		J. Aust. Math. Soc. 75 (2003), 1-21.	math.CA/0201220
Fuglede's conjecture is false in 5 and higher dimensions		Math. Res. Letters 11 (2004), 251-258	math.CA/0306134
An uncertainty principle for cyclic groups of prime order		Math. Res. Letters 12 (2005), 121-127	math.CA/0308286
The Brascamp--Lieb Inequalities: Finiteness, Structure and Extremals	Jon Bennett Tony Carbery Michael Christ	to appear, GAFA	math.MG/0505065
Finiteness bounds for Holder-Brascamp-Lieb multilinear inequalities	Jon Bennett Tony Carbery Michael Christ	Submitted,  Math. Res. Letters	math.CA/0505691
A quantitative version of the Besicovitch projection theorem via multiscale analysis		Submitted, Proc. Lond. Math. Soc.	math.CA/0706.2646 discussion

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

• Harmonic analysis [discussion]
• The Fourier transform [discussion]
  

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