Weighted Hardy–Rellich Inequality for Dunkl Operators

Jielin Lyu, Yongyang Jin, Shoufeng Shen and Li Tang ()
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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

Mathematics, 2023, vol. 11, issue 6, 1-12

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.

Keywords: Hardy inequalities; Hardy–Rellich inequalities; Dunkl operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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