Mathematics (Mar 2023)

Weighted Hardy–Rellich Inequality for Dunkl Operators

  • Jielin Lyu,
  • Yongyang Jin,
  • Shoufeng Shen,
  • Li Tang

DOI
https://doi.org/10.3390/math11061487
Journal volume & issue
Vol. 11, no. 6
p. 1487

Abstract

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In this paper, we proved a weighted Hardy–Rellich inequality for Dunkl operators based on the spherical h-harmonic decomposition theory of Dunkl operators. Moreover, we obtained the explicit constant of the inequalities, which is optimal in some cases. Our results extend some known inequalities.

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