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Weighted Hardy–Rellich Inequality for Dunkl Operators

Author

Listed:
  • Jielin Lyu

    (School of Continuing Education, Zhejiang Business College, Hangzhou 310053, China)

  • Yongyang Jin

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Shoufeng Shen

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Li Tang

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

Abstract

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.

Suggested Citation

  • Jielin Lyu & Yongyang Jin & Shoufeng Shen & Li Tang, 2023. "Weighted Hardy–Rellich Inequality for Dunkl Operators," Mathematics, MDPI, vol. 11(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1487-:d:1100877
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