HARDY INEQUALITIES WITH HI-POTENTIAL INVOLVED DUNKL OPERATOR
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Abstract
We prove a Hardy-type inequalities in Dunkl setting, integrated with an HI-potential. Our approach utilizes the h-harmonic expansion of functions and integrating techniques such as integral transformations, spherical coordinate formulas, and separation of variables, we derive the main result presented in Theorem 1. These outcomes build upon and extend the foundational work of Ghoussoub and Moradifam (2013), which addressed Hardy-type inequalities involving the Laplace operator and the Lebesgue measure in conjunction with an HI-potential. Consequently, our findings advance the generalization of Hardy inequality within broader context of Dunkl theory. Moreover, this research carries substantial implications for analyzing differential equations and partial differential equations that exhibit singularities, thereby providing enhanced understanding of the qualitative properties and behaviors of solutions in these equation classes. This extension not only refines existing inequalities but also opens avenues for applications in mathematical physics and functional analysis.
Keywords
best constant, Hardy inequality, HI-potential
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References
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