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.
M. Bohner and S. H. Saker, "Gehring Inequalities on Time Scales," Journal of Computational Analysis and Applications, vol. 28, no. 1, pp. 11 - 23, Eudoxus Press, LLC, Jan 2020.
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)
Article - Journal
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01 Jan 2020