Super Poincar\'e inequalities, Orlicz norms and essential spectrum
Functional Analysis
2011-01-25 v1 Probability
Spectral Theory
Abstract
We prove some results about the super Poincar\'e inequality (SPI) and its relation to the spectrum of an operator: we show that it can be alternatively written with Orlicz norms instead of L1 norms, and we use this to give an alternative proof that a bound on the bottom of the essential spectrum implies a SPI. Finally, we apply these ideas to give a spectral proof of the log Sobolev inequality for the Gaussian measure.
Keywords
Cite
@article{arxiv.0910.4768,
title = {Super Poincar\'e inequalities, Orlicz norms and essential spectrum},
author = {Pierre-André Zitt},
journal= {arXiv preprint arXiv:0910.4768},
year = {2011}
}
Comments
14 p