Super Poincaré inequalities, Orlicz norms and essential spectrum

Pierre-André Zitt (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: Super Poincaré inequality; Essential spectrum; measure–capacity inequality

Domaines: Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]; Probabilités [math.PR]

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