HARDY INEQUALITIES WITH HI-POTENTIAL INVOLVED DUNKL OPERATOR

Tóm tắt

We prove a Hardy-type inequalities in Dunkl setting, integrated with an HI-potential. Our
approach utilizes the h-harmonic expansion of functions 2()k fLm ä 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.