Phase space localizing operators
Classical Analysis and ODEs
2024-02-20 v3
Abstract
We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase plane projections of Muscalu, Tao and the third author in one dimension. The motivation for such operators comes from time-frequency analysis. They are used in particular to prove uniform estimates for multilinear modulation invariant operators.
Cite
@article{arxiv.2210.16164,
title = {Phase space localizing operators},
author = {Marco Fraccaroli and Olli Saari and Christoph Thiele},
journal= {arXiv preprint arXiv:2210.16164},
year = {2024}
}
Comments
v3: added a reference to the application of the result. "Outside of the tree" item of the main theorem now has a slightly stronger form (contained in the old proof but not in the old statement)