Hardy type inequalities and Gaussian measure

Barbara Brandolini; Francesco Chiacchio; Cristina Trombetti

doi:10.3934/cpaa.2007.6.411

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2007, Volume 6, Issue 2: 411-428. Doi: 10.3934/cpaa.2007.6.411

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Hardy type inequalities and Gaussian measure

1.
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, via Cintia, 80126 Napoli

Received: June 2006

Revised: January 2007

Published: June 2007

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Abstract

In this paper we prove some improved Hardy type inequalities with respect to the Gaussian measure. We show that they are strictly related to the well-known Gross Logarithmic Sobolev inequality. Some applications to elliptic P.D.E.'s are also given.

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Mathematics Subject Classification: Primary: 46E30, 35J70; Secondary: 35J30.

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