Small Divisor problems and $A_p$ weights with an application
Analysis of PDEs
2025-02-27 v2
Abstract
We establish a link between Muckenhoupt weights and a means to address small divisor problems. We use this link to obtain a quantitative version of the Ehrenpreis-Malgrange theorem of local solvability for constant coefficient PDE. We give an example as to how our theorem applies. In our quantitative version of the Ehrenpreis-Malgrange theorem, the loss of derivatives in the solvability estimate is measured in the scale of Sobolev spaces via the use of Muckenhoupt A_p weights. A part of our results are global in nature.
Cite
@article{arxiv.2407.19522,
title = {Small Divisor problems and $A_p$ weights with an application},
author = {Sagun Chanillo},
journal= {arXiv preprint arXiv:2407.19522},
year = {2025}
}
Comments
This is the accepted version of the paper incorporating various revisions suggested by the referee. The paper will appear in a special volume for Bernard Helffer in Pure and Applied Functional Analysis(PAFA)