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

arXiv:9910039 

Bilinear: dvi

Uniform estimates on paraproducts

Camil Muscalu 

Christoph Thiele

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

arXiv:0106092

Uniform estimates for multi-linear operators with modulation symmetry

Camil Muscalu 

Christoph Thiele

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

arXiv:0107059

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

Camil Muscalu 

Christoph Thiele

Math. Annalen 329 (2004), 401-426

arXiv:0102083

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

Camil Muscalu 

Christoph Thiele

Math. Annalen 329 (2004), 427-461

arXiv:0102084

Multi-linear multipliers associated to simplexes of arbitrary length

Camil Muscalu 

Christoph Thiele

SubmittedAnalysis & PDE

arXiv:0712.2420

discussion

A discrete model for the bi-carleson operator

Camil Muscalu 

Christoph Thiele

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

arXiv:0201060

A counterexample to a multilinear endpoint question of Christ and Kiselev 

Camil Muscalu 

Christoph Thiele

Math. Res. Letters 10 (2003), 237-246

arXiv:0108156

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

Camil Muscalu 

Christoph Thiele

Nonlinearity 19 (2003), 219-246

arXiv:0205139

Multilinear interpolation between adjoint operators

Loukas Grafakos

J. Funct. Anal. 199 (2003), 379-385

arXiv:0111141

L^p bounds for a maximal dyadic sum operator

Loukas Grafakos 

Erin Terwilleger

Math. Z. 246 (2004), 321-337

arXiv:0212164

Bi-parameter paraproducts

Camil Muscalu 

Jill Pipher 

Christoph Thiele

Acta Math. 193 (2004), 269–296

arXiv:0310367

On multilinear oscillatory integrals, nonsingular and singular

Michael Christ 

Xiaochun Li 

Christoph Thiele

Duke Math. J. 130 (2005), 321—351.

arXiv:0311039

Nonlinear Fourier Analysis

Christoph Thiele

To be submitted

arXiv:1201.5129

pdf

The Bi-Carleson operator

Camil Muscalu 

Christoph Thiele

GAFA 16 (2006), 230—277

arXiv:0409406

Multi-parameter paraproducts

Camil Muscalu 

Jill Pipher 

Christoph Thiele

Revista Mat. Iber. 22 (2006), 963-976

arXiv:0411607

Maximal multilinear operators

Ciprian Demeter

Christoph Thiele

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

arXiv:0510581

Breaking duality in the return times theorem

Ciprian Demeter

Michael Lacey

Christoph Thiele

Duke Math. J. 143 (2008), 281-355

arXiv: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

J. Europ. Math. Soc. 14 (2012), 421-464.

arxiv:0910.1555

discussion

Cancellation in the multilinear Hilbert transform

Collectanea Mathematica 67 (2016), 1-16

arXiv:1505.06479

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