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Affine Pólya-Szegö inequality on Steiner rearrangement in any codimension

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Abstract

The affine Polya-Szego inequality on the Steiner rearrangement in any codimension is proved. We not only define k-Orlicz-Sobolev ball on Sobolev functions and prove corresponding affine Polya-Szego inequality, but also define k-Orlicz-Sobolev ball on functions of bounded variation and prove the corresponding affine Polya-Szego inequality.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11971080), the Basic and Advanced Research Project of Chongqing, Chongqing Science and Technology Commission (Grant Nos. cstc2015jcyjA00009 and cstc2018jcyjAX0790) and Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1500628).

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  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Youjiang Lin

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Lin, Y. Affine Pólya-Szegö inequality on Steiner rearrangement in any codimension. Sci. China Math. 65, 517–538 (2022). https://doi.org/10.1007/s11425-020-1760-2

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