Super Poincaré inequalities, Orlicz norms and essential spectrum

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.
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Contributor : Pierre-André Zitt <>
Submitted on : Sunday, October 25, 2009 - 3:12:07 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Thursday, June 17, 2010 - 5:57:58 PM

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Pierre-André Zitt. Super Poincaré inequalities, Orlicz norms and essential spectrum. Potential Analysis, Springer Verlag, 2010, Online First, http://www.springerlink.com/content/e762065066852676/. ⟨10.1007/s11118-010-9203-z⟩. ⟨hal-00426367⟩

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