Abstract

In this paper, we first prove a new dynamic inequality based on an application of the time scales version of a Hardy-type inequality. Second, by employing the obtained inequality, we prove several Gehring-type inequalities on time scales. As an application of our Gehring-type inequalities, we present some interpolation and higher integrability theorems on time scales. The results as special cases, when the time scale is equal to the set of all real numbers, contain some known results, and when the time scale is equal to the set of all integers, the results are essentially new.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Gehring's inequality; Hardy-type inequality; Higher integrability; Interpolation; Reversed Hölder inequality; Time scales

International Standard Serial Number (ISSN)

1521-1398

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2020 Eudoxus Press, LLC, All rights reserved.

Included in

Mathematics Commons

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