Title :

Self-improving properties for abstract Poincaré type inequalities

Author(s) :

Bernicot, Frederic [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Martell, José Maria [Auteur]
Instituto de Ciencias Matemàticas [Madrid] [ICMAT]

Journal title :

Transactions of the American Mathematical Society

Pages :

4793-4835

Publisher :

American Mathematical Society

Publication date :

2015

ISSN :

0002-9947

Keyword(s) :

Self-improving properties
BMO and Lipschitz spaces
John-Nirenberg inequalities
generalized Poincaré-Sobolev inequalities
pseudo-Poincaré inequalities
semigroups

HAL domain(s) :

Mathématiques [math]/Analyse classique [math.CA]

English abstract : [en]

We study self-improving properties in the scale of Lebesgue spaces of generalized Poincaré inequalities in the Euclidean space. We present an abstract setting where oscillations are given by certain operators (e.g., ...
Show more >We study self-improving properties in the scale of Lebesgue spaces of generalized Poincaré inequalities in the Euclidean space. We present an abstract setting where oscillations are given by certain operators (e.g., approximations of the identity, semigroups or mean value operators) that have off-diagonal decay in some range. Our results provide a unified theory that is applicable to the classical Poincaré inequalities and furthermore it includes oscillations defined in terms of semigroups associated with second order elliptic operators as those in the Kato conjecture. In this latter situation we obtain a direct proof of the John-Nirenberg inequality for the associated BMO and Lipschitz spaces of [HMay,HMM].Show less >

Language :

Anglais

Popular science :

Non

Comment :

42 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL