Higher Summability and Discrete Weighted Muckenhoupt and Gehring Type Inequalities. Issue 4 (11th March 2019) - Saker, S. H.; Kubiaczyk, I.
Abstract: In this paper, we prove some reverse discrete inequalities with weights of Muckenhoupt and Gehring types and use them to prove some higher summability theorems on a higher weighted space l_w^p(N) form summability on the weighted space l_w^q(N) when p > q . The proofs are obtained by employing new discrete weighted Hardy's type inequalities and their converses for non-increasing sequences, which, for completeness, we prove in our special setting. To the best of the authors' knowledge, these higher summability results have not been considered before. Some numerical results will be given for illustration.