Convolution kernels of 2D Fourier multipliers based on real analytic functions
Classical Analysis and ODEs
2016-06-28 v3
Abstract
In this paper, estimates are proven for convolution kernels associated to multipliers from a reasonably general class of compactly supported two-dimensional functions constructed out of real-analytic functions. These estimates are both for overall decay rate and decay rate in specific directions. The estimates are sharp for a certain range of exponents appearing in the theorems.
Cite
@article{arxiv.1605.08136,
title = {Convolution kernels of 2D Fourier multipliers based on real analytic functions},
author = {Michael Greenblatt},
journal= {arXiv preprint arXiv:1605.08136},
year = {2016}
}
Comments
25 pages. v3: In the earlier versions, the roles of v and v^{\perp} were opposite in Lemma 1.2 and Theorems 1.3-1.4. This version switches them in various places to make the notation consistent