Volume 18, 2014
|Page(s)||503 - 513|
|Published online||10 October 2014|
A simple approach to functional inequalities for non-local Dirichlet forms
School of Mathematics and Computer Science, Fujian Normal University, 350007
Fuzhou, P.R. China
With direct and simple proofs, we establish Poincaré type inequalities (including Poincaré inequalities, weak Poincaré inequalities and super Poincaré inequalities), entropy inequalities and Beckner-type inequalities for non-local Dirichlet forms. The proofs are efficient for non-local Dirichlet forms with general jump kernel, and also work for Lp(p> 1) settings. Our results yield a new sufficient condition for fractional Poincaré inequalities, which were recently studied in [P.T. Gressman, J. Funct. Anal. 265 (2013) 867–889. C. Mouhot, E. Russ and Y. Sire, J. Math. Pures Appl. 95 (2011) 72–84.] To our knowledge this is the first result providing entropy inequalities and Beckner-type inequalities for measures more general than Lévy measures.
Mathematics Subject Classification: 60G51 / 60G52 / 60J25 / 60J75
Key words: Non-local Dirichelt forms; Poincaré type inequalities; entropy inequalities; Beckner-type inequalities
© EDP Sciences, SMAI 2014
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.