Super Poincaré Inequalities, Orlicz Norms and Essential Spectrum
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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 L 1 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.
KeywordsSuper Poincaré inequality Essential spectrum Measure–capacity inequality
Mathematics Subject Classifications (2010)39B62 47A10 47D07
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