On Some Inequalities for Exponentially Weighted Fractional Hardy Operators with ∆-Integral Calculus

Abstract

Dynamic equations, inequalities, and operators are the indispensable cornerstones of harmonic analysis and time-scale calculus. Undoubtedly, one of the most important of these operators and inequalities is the Hardy operator and inequality. Because especially when we say variable exponent Lebesgue space, the first thing that comes to our mind is the Hardy operator. We know that the topics in question have many applications in different scientific fields. In this paper, some inequalities will be proved for variable exponentially weighted Hardy operators with ∆-integral calculus.