Some characterizations of dynamic weighted Hardy-type inequalities with applications

The pairs of non-negative weights (u, v) for which dynamic inequalities of Hardy's type on a time scale T hold are (p, q) characterized in two different time-scale spaces Lpv(T) and Lqu(T ). We consider two distinct scenarios of values of the exponents p and q. These results complement the classical strong (p, p) results and their generalizations considered by some authors. For applications, we provide the corresponding continuous and discrete results when T = R, T = N, and T is the quantum space $N0 for $ > 1, respectively. As special cases, we capture some consequences for the results obtained by Anderson, Heinig, Kufner, Flett, and Saker.& COPY; 2023 Elsevier Inc. All rights reserved.