Weighted Hardy–Rellich Inequality for Dunkl Operators

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