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arXiv · 2309.02597

A unified approach to self-improving property via K-functionals

Oscar Dominguez·Yinqin Li·Sergey Tikhonov·Dachun Yang·Wen Yuan
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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.

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Oscar Dominguez, Yinqin Li, Sergey Tikhonov, Dachun Yang, Wen Yuan. 2023-09-05. A unified approach to self-improving property via K-functionals. https://arxiv.org/abs/2309.02597

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