Progress on Hardy-type Inequalities
Probability
2014-12-02 v1 Classical Analysis and ODEs
Functional Analysis
Abstract
This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in terms of the -theory. A crucial application of a result by Fukushima and Uemura (2003) is included. In the second section, the non-linear case (a general Hardy-type inequality) is handled with a direct and analytic proof. In the last section, it is illustrated that the basic estimates presented in the first two sections can still be improved considerably.
Cite
@article{arxiv.1412.0076,
title = {Progress on Hardy-type Inequalities},
author = {Mu-Fa Chen},
journal= {arXiv preprint arXiv:1412.0076},
year = {2014}
}
Comments
13 pages, 5 figures, Festschrift Masatoshi Fukushima: In Honor of Masatoshi Fukushima's Sanju. World Scientific, 2015