Sharp quantitative integral inequalities for harmonic extensions
Analysis of PDEs
2025-08-14 v1 Classical Analysis and ODEs
Functional Analysis
Abstract
We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and the optimal stability exponent. This stability exponent is not necessarily equal to 2, displaying the same phenomenon that Figalli and Zhang observed for the -Sobolev inequality.
Keywords
Cite
@article{arxiv.2508.09940,
title = {Sharp quantitative integral inequalities for harmonic extensions},
author = {Rupert L. Frank and Jonas W. Peteranderl and Larry Read},
journal= {arXiv preprint arXiv:2508.09940},
year = {2025}
}
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39 pages