Endpoint sparse domination for classes of multiplier transformations
Classical Analysis and ODEs
2024-05-10 v2
Abstract
We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipliers based on natural localized norms which express appropriate endpoint regularity hypotheses. The applications include new and optimal sparse bounds for classical oscillatory multipliers and multi-scale versions of radial bump multipliers.
Cite
@article{arxiv.2212.12437,
title = {Endpoint sparse domination for classes of multiplier transformations},
author = {David Beltran and Joris Roos and Andreas Seeger},
journal= {arXiv preprint arXiv:2212.12437},
year = {2024}
}
Comments
Typo in Theorem 1.3 corrected (the result is proved for $1<p<2<q\le p'$ with the endpoint $q=p'$ included). 55 pages, 1 figure