Some New Hardy-Type Inequalities with Negative Parameters on Time Scales

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Irena Jadlovská
Ahmed I. Saied

Abstract

In this paper, we present new Hardy-type inequalities with negative parameters on a time scale T. The adopted approach draws upon the use of a reversed Hölder dynamic inequality, a chain rule, and the integration by parts rule on time scales. In the continuous case, our results contain integral inequalities due to Benaissa and Budak, while in the discrete case, the obtained inequalities are essentially new. Additionally, we demonstrate the applicability of our results in the quantum case.

Recommended Citation

M. Bohner et al., "Some New Hardy-Type Inequalities with Negative Parameters on Time Scales," Qualitative Theory of Dynamical Systems, vol. 24, no. 2, article no. 72, Springer; Birkhäuser Verlag, Apr 2025.

The definitive version is available at https://doi.org/10.1007/s12346-025-01231-z

Department(s)

Mathematics and Statistics

Publication Status

Open Access

Comments

European Commission, Grant 09I03-03-V03-00075

Keywords and Phrases

Dynamic inequalities on time scales; Hardy-type inequalities; Negative parameter; Reversed Hölder's inequality

International Standard Serial Number (ISSN)

1662-3592; 1575-5460

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Springer; Birkhäuser Verlag, All rights reserved.

Publication Date

01 Apr 2025