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Potential Analysis

, Volume 35, Issue 1, pp 51–66 | Cite as

Super Poincaré Inequalities, Orlicz Norms and Essential Spectrum

  • Pierre-André ZittEmail author
Article

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 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.

Keywords

Super Poincaré inequality Essential spectrum Measure–capacity inequality 

Mathematics Subject Classifications (2010)

39B62 47A10 47D07 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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