Preprints in multilinear analysis

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Math 254A home page - Harmonic analysis in the phase plane. (2001)

Papers, and projects close to completion

Title	With	Status	Download
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), 269–296	math.CA/0310367
On multilinear oscillatory integrals, nonsingular and singular	Michael Christ Xiaochun Li Christoph Thiele	Duke Math. J. 130 (2005), 321—351.	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), 230—277	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

• Boundedness of the trilinear Hilbert transform