Geodesic
A simple approach to functional inequalities for non-local Dirichlet forms
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 503-513

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/ps/2013048
Classification : 60G51, 60G52, 60J25, 60J75
Keywords: non-local dirichelt forms, Poincaré type inequalities, entropy inequalities, Beckner-type inequalities 
@article{PS_2014__18__503_0,
     author = {Wang, Jian},
     title = {A simple approach to functional inequalities for non-local {Dirichlet} forms},
     journal = {ESAIM: Probability and Statistics},
     pages = {503--513},
     publisher = {EDP-Sciences},
     volume = {18},
     year = {2014},
     doi = {10.1051/ps/2013048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2013048/}
}
TY  - JOUR
AU  - Wang, Jian
TI  - A simple approach to functional inequalities for non-local Dirichlet forms
JO  - ESAIM: Probability and Statistics
PY  - 2014
SP  - 503
EP  - 513
VL  - 18
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2013048/
DO  - 10.1051/ps/2013048
LA  - en
ID  - PS_2014__18__503_0
ER  - 
%0 Journal Article
%A Wang, Jian
%T A simple approach to functional inequalities for non-local Dirichlet forms
%J ESAIM: Probability and Statistics
%D 2014
%P 503-513
%V 18
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2013048/
%R 10.1051/ps/2013048
%G en
%F PS_2014__18__503_0
Wang, Jian. A simple approach to functional inequalities for non-local Dirichlet forms. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 503-513. doi: 10.1051/ps/2013048

Cité par Sources :