Super Poincaré inequalities, Orlicz norms and essential spectrum
arXiv:0910.4768 · doi:10.1007/s11118-010-9203-z
Abstract
We prove some results about the super Poincaré 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.
14 p