Integral isoperimetric transference and dimensionless Sobolev inequalities

We introduce the concept of Gaussian integral isoperimetric transfer and show how it can be applied to obtain a new class of sharp Sobolev-Poincaré inequalities with constants independent of the dimension. In the special case of Lq spaces on the unit n-dimensional cube our results extend the recent...

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Bibliographic Details
Authors: Martín i Pedret, Joaquim|||0000-0002-7467-787X, Milman, Mario|||0000-0003-3735-8009
Format: article
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:268403
Online Access:https://ddd.uab.cat/record/268403
https://dx.doi.org/urn:doi:10.1007/s13163-014-0153-7
Access Level:Open access
Keyword:Extrapolation
Isoperimetric inequalities
Sobolev inequalities
Symmetrization
Description
Summary:We introduce the concept of Gaussian integral isoperimetric transfer and show how it can be applied to obtain a new class of sharp Sobolev-Poincaré inequalities with constants independent of the dimension. In the special case of Lq spaces on the unit n-dimensional cube our results extend the recent inequalities that were obtained in Fiorenza et al. (2012) using extrapolation.