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$%J. Kališ and M. Milman, Symmetrization and Sharp Sobolev Inequalities in Metric Spaces , Rev. Mat. Complut. 22 (2009), no. 2, 499–515.%$

Symmetrization and Sharp Sobolev Inequalities in Metric Spaces

Jan KALIŠ and Mario MILMAN

Department of Mathematics

Florida Atlantic University

Boca Raton, Fl 33431 — USA

kalis@math.fau.edu extrapol@bellsouth.net

Received: January 22, 2009
Accepted: March 6, 2009

ABSTRACT

We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and Faber-Krahn estimates for Hörmander vector fields.

Key words: Sobolev, embedding, metric, vector fields, symmetrization.
2000 Mathematics Subject Classification: Primary: 46E30, 26D10.