Fractional Poincaré inequalities for general measures

By Clément Mouhot, E. Russ, Yannick Sire. 2009

47 citations recorded by the source corpus.

Abstract We prove a fractional version of Poincare inequalities in the context of R n endowed with a fairly general measure. Namely we prove a control of an L 2 norm by a non-local quantity, which plays the role of the gradient in the standard Poincare inequality. The assumption on the measure is the fact that it satisfies the classical Poincare inequality, so that our result is an improvement of the latter inequality. Moreover we also quantify the tightness at infinity provided by the control on the fractional derivative in terms of a weight growing at infinity. The proof goes through the introduction of the generator of the Ornstein–Uhlenbeck semigroup and some careful estimates of its powers. To our knowledge this is the first proof of fractional Poincare inequality for measures more general than Levy measures.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6686d1f757af2231e83fc643e280165d98c82f33

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Exponential Stability of Slowly Decaying Solutions to the Kinetic-Fokker-Planck Equation (2014, background): “oof of Lemma 3.6 is classical. We refer to [2] for a comprehensive proof of (3.13). For the sake of completeness, we present a quantitative proof of (3.14) as a consequence of (3.13) in the spirit of [21]. STABILITY OF SLOWLY DECAYING SOLUTIONS... 17 On the one hand, by developing the LHS term, we ﬁ”