Higher Summability and Discrete Weighted Muckenhoupt and Gehring Type Inequalities. Issue 4 (11th March 2019)

• Record Type: Journal Article
• Authors: Saker, S. H.; Kubiaczyk, I.
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 4(2019)
• Page Start: 949
• Page End: 973
• Publication Date: 2019-03-11
• Subjects: reverse Hölder inequality, -- Hardy's type inequality, -- interpolation, -- weighted Muckenhoupt's inequality, -- weighted Gehring's inequality, -- higher summability; Primary 26D07, -- 42B25, -- 42C10, -- 42A24; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091519000014
• Languages: English
• ISSNs: 0013-0915

Abstract

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 $l_{w}^{p}({\open N})$ form summability on the weighted space $l_{w}^{q}({\open N})$ 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.