Super-Poincaré and Nash-type inequalities for Subordinated Semigroups

Abstract

We prove that if a super-Poincaré inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincaré inequality for $-g(A)$ with any Bernstein function $g$. We also study the converse statement. We deduce similar results for the Nash-type inequality. Our results applied to fractional powers of $A$ and to $\log (I+A)$ and thus generalize some results of Biroli and Maheux, and Wang 2007. We provide several examples.

submitted. 23p. no figure. Title slightly changed. Results and text improved

References in corpus (1)

• Poincaré inequality and the Lp convergence of semi-groups

Cited by in corpus (1)

• Functional Inequalities for Stable-Like Dirichlet Forms