Nash-type inequalities, Super-Poincaré inequalities for Subordinated Semigroups

Details Nash-type inequalities, Super-Poincaré inequalities for Subordinated Semigroups Nash-type inequalities, Super-Poincaré inequalities for Subordinated Semigroups

2011-05-16

arxiv.org/abs/1105.3095v1

Mathematics

Functional Analysis

submitted. 22p. no figure

Scientific paper

We prove that Super-Poincar\'e inequality for a generator A of a (sub)-Markovian semi-group (T_t) implies a corresponding Super-Poincar\'e inequality for g(A) with g a Bernstein function. We deduce a similar result when Super-Poincar\'e inequality is replaced by Nash-type inequality and prove that if D is a Nash function for A then g o D is essentially a Nash function for g(A). In particular, our results apply to fractional powers of A and log(id + A) generalizing some results of [B-M1] and [W1]. We provides examples.

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