Small Divisor problems and $A_p$ weights with an application

Sagun Chanillo

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arXiv · 2407.19522

Small Divisor problems and $A_p$ weights with an application

Sagun Chanillo

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Abstract

We establish a link between Muckenhoupt $A_p$ 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.

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Sagun Chanillo. 2024-07-28. Small Divisor problems and $A_p$ weights with an application. https://arxiv.org/abs/2407.19522

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