A Note on the Extremizers for a Nonlinear Hardy-Littlewood-Sobolev Inequality

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Abstract

The extremizers of a nonlinear Hardy-Littlewood-Sobolev inequality will be classified by making use of the Frank-Lieb argument, via the stereographic projection and spherical harmonic.

Keywords:

Funk-Hecke formula Hardy-Littlewood-Sobolev inequality Spherical harmonic functions Stereographic projection

Author Biographies

  • Xingdong Tang

    School of Mathematics and Statistics, Nanjing Univeristy of  Information Science and Technology, Nanjing 210044, China

  • Yang Zhang

    School of Mathematics and Statistics, Nanjing Univeristy of  Information Science and Technology, Nanjing 210044, China

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DOI

10.4208/JICS-2025-006