English

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 pp-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}
}

Comments

39 pages

R2 v1 2026-07-01T04:48:25.389Z