Novel generalized inequalities involving a general Hardy operator with multiple variables and general kernels on time scales

Abstract

This paper introduced novel multidimensional Hardy-type inequalities with general kernels on time scales, extending existing results in the literature. We established generalized inequalities involving a general Hardy operator with multiple variables and kernels on arbitrary time scales. Our findings not only encompassed known results in the realm of real numbers ($ \mathbb{T=R} $), but also provided refinements and generalizations thereof. The proposed inequalities offered versatile applications in mathematical analysis and beyond, contributing to the ongoing exploration of inequalities on diverse time scales.

Keywords

• hardy type inequality
• hardy's operator
• weighted functions
• inequalities with kernels
• time scales