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Super Poincaré inequalities, Orlicz norms and essential spectrum

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.

preprint2009arXivOpen access
Pierre-André Zitt
math.PRmath.FAmath.SP
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Pierre-André Zitt

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