Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization

The Fractional Poincare’ inequalities in R n are endowed with a fairly general sequence measure. We show a control of L 2 norm by a non–Local quantity. The assumption on the sequence measure is that it satisfies the classical Poincare’ inequality, with general results. We also verify quantity of the tightness at infinity provided by the control on the fractional derivative in terms of a sequence of a weight growing at infinity. The illustration goes to the generator of the Ornstein-Uhlenbeck semi group and some estimates of its powers.