Bibliographic Details
| Title: |
A unified approach to self-improving property via K-functionals |
| Authors: |
Dominguez, Oscar, Li, Yinqin, Tikhonov, Sergey, Yang, Dachun, Yuan, Wen |
| Publication Year: |
2023 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Functional Analysis, Mathematics - Classical Analysis and ODEs |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2309.02597 |
| Accession Number: |
edsarx.2309.02597 |
| Database: |
arXiv |
