Abstract
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 Lvp(T) and Luq(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 ℓN0 for ℓ>1, respectively. As special cases, we capture some consequences for the results obtained by Anderson, Heinig, Kufner, Flett, and Saker.
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