TY - JOUR
T1 - Weighted sobolev inequalities in CD(0, n) spaces
AU - Tewodrose, David
N1 - Publisher Copyright:
© The authors. Published by EDP Sciences, SMAI 2021.
PY - 2021
Y1 - 2021
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.
KW - Heat kernel
KW - Metric measure spaces#curvature-dimension conditions
KW - Sobolev inequalities
UR - http://www.scopus.com/inward/record.url?scp=85101981345&partnerID=8YFLogxK
U2 - 10.1051/cocv/2020080
DO - 10.1051/cocv/2020080
M3 - Article
AN - SCOPUS:85101981345
VL - 27
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
SN - 1262-3377
M1 - 2020080
ER -