Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
Martín i Pedret, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Milman, Mario (Instituto Argentino de Matemática)

Date:	2016
Abstract:	We extend the recent L1 uncertainty inequalities obtained in [13] to the metric setting. For this purpose we introduce a new class of weights, named isoperimetric weights, for which the growth of the measure of their level sets μ can be controlled by rI(r), where I is the isoperimetric profile of the ambient metric space. We use isoperimetric weights, new localized Poincaré inequalities, and interpolation, to prove Lp, 1≤p<∞, uncertainty inequalities on metric measure spaces. We give an alternate characterization of the class of isoperimetric weights in terms of Marcinkiewicz spaces, which combined with the sharp Sobolev inequalities of [20], and interpolation of weighted norm inequalities, give new uncertainty inequalities in the context of rearrangement invariant spaces.
Grants:	Ministerio de Economía y Competitividad MTM2013-44304-P Ministerio de Economía y Competitividad MTM2013-40985-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-289
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Isoperimetric inequalities ; Isoperimetric weight ; Uncertainty inequalities
Published in:	Journal of functional analysiss, Vol. 270, Issue 9 (May 2016) , p. 3307-3343, ISSN 1096-0783

DOI: 10.1016/j.jfa.2016.02.016

Postprint 33 p, 597.7 KB

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