Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 877–897

SYMMETRIZATION INEQUALITIES FOR PROBABILITY METRIC SPACES WITH CONVEX ISOPERIMETRIC PROFILE

Joaquim Martín and Walter A. Ortiz

Universitat Autònoma de Barcelona, Department of Mathematics
08193 Bellaterra (Barcelona), Spain; jmartin 'at' mat.uab.cat

Universitat Autònoma de Barcelona, Department of Mathematics
08193 Bellaterra (Barcelona), Spain; waortiz 'at' mat.uab.cat

Abstract. We obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp Sobolev–Poincaré and Nash inequalities.

2010 Mathematics Subject Classification: Primary 46E35.

Key words: Sobolev–Poincaré inequalities, Nash inequalities, symmetrization, isoperimetric convex profile.

Reference to this article: J. Martín and W. A. Ortiz: Symmetrization inequalities for probability metric spaces with convex isoperimetric profile. Ann. Acad. Sci. Fenn. Math. 45 (2020), 877–897.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4548