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Affine Orlicz Pólya–Szegö Principles and Their Equality Cases

  • Published:2019-04-02 Issue:9 Volume:2021 Page:7159-7204
  • ISSN:1073-7928
  • Container-title:International Mathematics Research Notices
  • language:en
  • Short-container-title:

Author:

Lin Youjiang1,Xi Dongmeng23

Affiliation:

1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, PR China

2. Department of Mathematics, Shanghai University, Shanghai, China

3. School of Mathematical Sciences, Fudan University, Shanghai, China, Shanghai, PR China

Abstract

Abstract The conjecture about the Orlicz Pólya–Szegö principle posed in [42] is proved. The cases of equality are characterized in the affine Orlicz Pólya–Szegö principle with respect to Steiner symmetrization and Schwarz spherical symmetrization.

Funder

Cognitive Sciences and Technologies Council

Chongqing Municipal Education Commission

Shanghai Sailing Program

National Natural Science Foundation of China

Chinese Post-doctoral Innovation Talent Support Program

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference72 articles.

1. Stability of Pólya-Szegö inequality for log-concave functions;Barchiesi;J. Funct. Anal.,2014

2. Symmetrization in geometry;Bianchi;Adv. Math.,2017

3. Stronger versions of the Orlicz-petty projection inequality;Böröczky;J. Differ. Geom.,2013

4. The log-Brunn–Minkowski inequality;Böröczky;Adv. Math.,2012

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1. Orlicz affine isoperimetric inequalities for star bodies;Advances in Applied Mathematics;2022-03

2. Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $;AIMS Mathematics;2022

3. Affine Pólya-Szegö inequality on Steiner rearrangement in any codimension;Science China Mathematics;2021-08-05

4. On the Mixed Pólya-Szegö Principle;Acta Mathematica Sinica, English Series;2021-03-25

5. The affine Orlicz Pólya–Szegö principle on $$BV(\Omega )$$;Calculus of Variations and Partial Differential Equations;2019-10
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