Camil Muscalu

Multi-linear operators given by singular multipliers

We prove L^p estimates for a large class of multi-linear operators, which includes the multi-linear paraproducts studied by Coifman and Meyer, as well as the bilinear Hilbert transform.

Bi-parameter paraproducts

In the first part of the paper we prove a bi-parameter version of a well known multilinear theorem of Coifman and Meyer. As a consequence, we generalize the Kato-Ponce inequality in nonlinear PDE, obtaining a fractional Leibnitz rule for derivatives in the

Multi-parameter paraproducts

x_1

Carleson measures, trees, extrapolation, and T(b) theorems

and

Variational estimates for paraproducts

x_2

Generalizations of the Carleson-Hunt theorem I. The classical singularity case

directions simultaneously. Then, we show that the double bilinear Hilbert transform does not satisfy any

Calderón commutators and the Cauchy integral on Lipschitz curves revisited III. Polydisc extensions

L^p

Radial limit of lacunary Fourier series with coefficients in non-commutative symmetric spaces

estimates.

Classical and Multilinear Harmonic Analysis: Frontmatter

We prove that classical Coifman-Meyer theorem holds on any polidisc Td or arbitrary dimension d = 1

Classical and Multilinear Harmonic Analysis: Acknowledgements

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of extrapolation for Carleson measures, as well as a two-sided local dyadic T(b) theorem which generalizes earlier T(b) theorems of David, Journe, Semmes, and Christ.