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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Multilinear operators given by singular multipliers

Camil Muscalu
Christoph Thiele

J. Amer. Math. Soc. 15 (2002), 469-496

math.CA/9910039
Bilinear: dvi

Uniform estimates on paraproducts

Camil Muscalu
Christoph Thiele

Journal d'Analyse de Jerusalem 87 (2002), 369-384

math.CA/0106092

Uniform estimates for multi-linear operators with modulation symmetry

Camil Muscalu
Christoph Thiele

Journal d'Analyse de Jerusalem 88 (2002), 255-309

math.CA/0107059

L^p estimates for the "biest" I.  The Walsh model.

Camil Muscalu
Christoph Thiele

Math. Annalen 329 (2004), 401-426

math.CA/0102083

L^p estimates for the "biest" II.  The Fourier model.

Camil Muscalu
Christoph Thiele

Math. Annalen 329 (2004), 427-461

math.CA/0102084

Multi-linear multipliers associated to simplexes of arbitrary length

Camil Muscalu
Christoph Thiele

Submitted, Analysis & PDE

arXiv:0712.2420
discussion

A discrete model for the bi-carleson operator

Camil Muscalu
Christoph Thiele

Geom. Func. Anal. 12 (2002), 1324-1364

math.CA/0201060

A counterexample to a multilinear endpoint question of Christ and Kiselev 

Camil Muscalu
Christoph Thiele

Math. Res. Letters 10 (2003), 237-246

math.CA/0108156

A Carleson-type theorem for a Cantor group model of the Scattering Transform

Camil Muscalu
Christoph Thiele

Nonlinearity 19 (2003), 219-246

math.CA/0205139

Multilinear interpolation between adjoint operators

Loukas Grafakos

J. Funct. Anal. 199 (2003), 379-385

math.FA/0111141

L^p bounds for a maximal dyadic sum operator

Loukas Grafakos
Erin Terwilleger

Math. Z. 246 (2004), 321-337

math.CA/0212164

Bi-parameter paraproducts

Camil Muscalu
Jill Pipher
Christoph Thiele

Acta Math. 193 (2004), 269296

math.CA/0310367

On multilinear oscillatory integrals, nonsingular and singular

Michael Christ
Xiaochun Li
Christoph Thiele

Duke Math. J. 130 (2005), 321351.

math.CA/0311039

Nonlinear Fourier Analysis

Christoph Thiele

to appear, Park City proceedings

pdf

The Bi-Carleson operator

Camil Muscalu
Christoph Thiele

GAFA 16 (2006), 230277

math.CA/0409406

Multi-parameter paraproducts

Camil Muscalu
Jill Pipher
Christoph Thiele

Revista Mat. Iber. 22 (2006), 963-976

math.CA/0411607

Maximal multilinear operators

Ciprian Demeter
Christoph Thiele

Trans. Amer. Math. Soc.,  360 (2008),  4989-5042

math.CA/0510581

Breaking duality in the return times theorem

Ciprian Demeter
Michael Lacey
Christoph Thiele

Duke Math. J. 143 (2008), 281-355

math.DS/0601455

The Walsh model for $M_2^*$ Carleson

Ciprian Demeter
Michael Lacey
Christoph Thiele

Revista Mat. Iber. 24 (2008), 721-744

arxiv:0712.1295
discussion

A variation norm Carleson theorem

Richard Oberlin

Andreas Seeger

Christoph Thiele

Jim Wright

Submitted, J. Europ. Math. Soc.

arxiv:0910.1555

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

An estimate for the bilinear Hilbert transform

A trilinear maximal inequality via arithmetic combinatorics

Open questions