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