Preprints in multilinear analysis
Math 254A home page - Harmonic analysis in the phase plane. (2001)
Papers, and projects close to completion
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J. Amer. Math. Soc. 15 (2002), 469-496 |
math.CA/9910039
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Uniform estimates on paraproducts |
Journal d'Analyse de |
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Uniform estimates for multi-linear operators with modulation symmetry |
Journal d'Analyse de |
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L^p estimates for the "biest" I. The Walsh model. |
Math. Annalen 329 (2004), 401-426 |
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L^p estimates for the "biest" II. The Fourier model. |
Math. Annalen 329 (2004), 427-461 |
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Multi-linear multipliers associated to simplexes of arbitrary length |
Submitted, Analysis & PDE |
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A discrete model for the bi-carleson operator |
Geom. Func. Anal. 12 (2002), 1324-1364 |
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A counterexample to a multilinear endpoint question of Christ and Kiselev |
Math. Res. Letters 10 (2003), 237-246 |
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A Carleson-type theorem for a Cantor group model of the Scattering Transform |
Nonlinearity 19 (2003), 219-246 |
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Multilinear interpolation between adjoint operators |
J. Funct. Anal. 199 (2003), 379-385 |
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L^p bounds for a maximal dyadic sum operator |
Math. Z. 246 (2004), 321-337 |
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Bi-parameter paraproducts |
Acta Math. 193 (2004), 269–296 |
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On multilinear oscillatory integrals, nonsingular and singular |
Duke Math. J. 130 (2005), 321—351. |
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Nonlinear Fourier Analysis |
to
appear, |
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The Bi-Carleson operator |
GAFA
16 (2006), 230—277 |
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Multi-parameter paraproducts |
Revista
Mat. Iber. 22 (2006), 963-976 |
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Maximal multilinear operators |
Trans. Amer.
Math. Soc., 360 (2008), 4989-5042 |
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Breaking duality in the return times theorem |
Duke Math. J. 143 (2008),
281-355 |
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| The Walsh model for $M_2^*$ Carleson | Ciprian
Demeter Michael Lacey Christoph Thiele |
to appear, Revista Mat. Iber. | arxiv:0712.1295 discussion |
Bilinear and multilinear estimates also arise in my papers
in PDE and in my papers
on the Kakeya and restriction
problems.
Multilinear expansions also arise in inverse scattering, but I have
classified
inverse scattering as a branch of PDE.
Some further papers dealing with more general aspects of harmonic
analysis 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.