Super Poincaré inequalities, Orlicz norms and essential spectrum

Details Super Poincaré inequalities, Orlicz norms and essential spectrum Super Poincaré inequalities, Orlicz norms and essential spectrum

2009-10-25

arxiv.org/abs/0910.4768v1

Potential Analysis (2010) Online First, http://www.springerlink.com/content/e762065066852676/

Mathematics

Functional Analysis

14 p

Scientific paper

10.1007/s11118-010-9203-z

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.

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