Results 21 to 28 of about 97,274 (28)

Maximal averages along a planar vector field depending on one variable [PDF]

arXiv, 2011
We prove (essentially) sharp $L^2$ estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines an understanding of such vector fields from earlier work of the author with a result of Nets Katz on directional maximal operators.
arxiv  

Single annulus $L^p$ estimates for Hilbert transforms along vector fields [PDF]

arXiv, 2011
We prove $L^p$, $p\in (1,\infty)$ estimates on the Hilbert transform along a one variable vector field acting on functions with frequency support in an annulus. Estimates when $p>2$ were proved by Lacey and Li in \cite{LL1}. This paper also contains key technical ingredients for a companion paper \cite{BT} with Christoph Thiele in which $L^p$ estimates
arxiv  

Bilinear dispersive estimates via space-time resonances. Part I : the one dimensional case [PDF]

arXiv, 2011
We prove new bilinear dispersive estimates. They are obtained and described via a bilinear time-frequency analysis following the space-time resonances method, introduced by Masmoudi, Shatah, and the second author. They allow us to understand the large time behavior of solutions of quadratic dispersive equations.
arxiv  

A remark on the reproducing kernel thesis for Hankel operators [PDF]

arXiv, 2011
We give a simple proof of the so called reproducing kernel thesis for Hankel ...
arxiv  

Mixed norm estimates for Hermite multipliers [PDF]

arXiv, 2013
In this article mixed norm estimates are obtained for some integral operators, from which those for the Hermite semigroup and the Bochner Riesz means associated with the Hermite expansions are deduced. Also, mixed norm estimates for the Littlewood Paley g functions and g* functions for the Hermite expansions are obtained, which lead to those for ...
arxiv  

Some endpoint estimates for bilinear paraproducts and applications [PDF]

arXiv, 2014
In this paper we establish the boundedness of bilinear paraproducts on local BMO spaces. As applications, we also investigate the boundedness of bilinear Fourier integral operators and bilinear Coifman-Meyer multipliers on these spaces and also obtain a certain end-point result concerning Kato-Ponce type estimates.
arxiv  

Multilinear Fourier multipliers on variable Lebesgue spaces [PDF]

arXiv, 2014
In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem of multipliers on variable exponent Lebesgue spaces.
arxiv  

The local symmetry condition in the Heisenberg group [PDF]

arXiv, 2018
I propose an analogue in the first Heisenberg group $\mathbb{H}$ of David and Semmes' local symmetry condition (LSC). For closed $3$-regular sets $E \subset \mathbb{H}$, I show that the (LSC) is implied by the $L^{2}(\mathcal{H}^{3}|_{E})$ boundedness of $3$-dimensional singular integrals with horizontally antisymmetric kernels, and that the (LSC ...
arxiv