A unified approach to self-improving property via K-functionals
Functional Analysis
2023-09-07 v1 Classical Analysis and ODEs
Abstract
In this paper we obtain new quantitative estimates that improve the classical inequalities: Poincar\'e-Ponce, Gaussian Sobolev, and John-Nirenberg. Our method is based on the K-functionals and allows one to derive self-improving type inequalities. We show the optimality of the method by obtaining new Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova limiting formulas. In particular, we derive these formulas for fractional powers of infinitesimal generators of operator semigroups on Banach spaces.
Cite
@article{arxiv.2309.02597,
title = {A unified approach to self-improving property via K-functionals},
author = {Oscar Dominguez and Yinqin Li and Sergey Tikhonov and Dachun Yang and Wen Yuan},
journal= {arXiv preprint arXiv:2309.02597},
year = {2023}
}