Weighted sobolev inequalities in CD(0, n) spaces

David Tewodrose

doi:10.1051/cocv/2020080

Weighted sobolev inequalities in CD(0, n) spaces

David Tewodrose

Mathematics

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Abstract

In this note, we prove global weighted Sobolev inequalities on non-compact CD(0, N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result from [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0, N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.

Original language	English
Article number	2020080
Number of pages	19
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	27
DOIs	https://doi.org/10.1051/cocv/2020080
Publication status	Published - 2021

Bibliographical note

Publisher Copyright:
© The authors. Published by EDP Sciences, SMAI 2021.

Keywords

Heat kernel
Metric measure spaces#curvature-dimension conditions
Sobolev inequalities

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abstract = "In this note, we prove global weighted Sobolev inequalities on non-compact CD(0, N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result from [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0, N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.",

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N2 - In this note, we prove global weighted Sobolev inequalities on non-compact CD(0, N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result from [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0, N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.

AB - In this note, we prove global weighted Sobolev inequalities on non-compact CD(0, N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result from [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0, N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.

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KW - Metric measure spaces#curvature-dimension conditions

KW - Sobolev inequalities

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JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 2020080

ER -

Weighted sobolev inequalities in CD(0, n) spaces

Abstract

Bibliographical note

Keywords

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