On the Mixed Pólya-Szegö Principle

Abstract

In this paper, the mixed Pólya-Szegö principle is established. By the mixed Pólya-Szegö principle, the mixed Morrey-Sobolev inequality and some new analytic inequalities are obtained.

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Acknowledgements

The first author would like to thank his postdoctoral adviser Professor Zizhou Tang for stimulating advises and suggestions. We thank anonymous referees for suggestions and comments.

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Correspondence to Jia Zu Zhou.

Additional information

The first author is supported in part by NSFC (Grant No. 12001291); The second author is supported in part by NSFC (Grant No. 12071318)

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Fang, N.F., Zhou, J.Z. On the Mixed Pólya-Szegö Principle. Acta. Math. Sin.-English Ser. (2021). https://doi.org/10.1007/s10114-021-0099-x

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Keywords

  • Pólya-Szegö principle
  • mixed Pólya-Szegö principle
  • Sobolev inequality
  • spherically symmetric rearrangement

MR(2010) Subject Classification

  • 52A22
  • 26D
  • 46E