Contributions to the Fractional Hardy Integral Inequality

Christophe Chesneau

doi:10.32323/ujma.1590154

EN

Contributions to the Fractional Hardy Integral Inequality

Abstract

This article makes three contributions to the fractional Hardy integral inequality. First, we refine an existing result in the literature by improving the main constant and relaxing some assumptions on the parameters. We then propose a fractional-type Hardy integral inequality for an under-studied case, with a significant adaptation of the existing general proof. Finally, a version of this result is established when the integral domain is finite. The proofs are given in detail, with the exact expression of the constants involved at each step. We also mention that almost no intermediate results are used.

Keywords

Fractional Hardy integral inequality, Fubini-Tonelli integral theorem, Hardy integral inequality, Integral inequalities

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Christophe Chesneau ^*
0000-0002-1522-9292
France

Early Pub Date

February 23, 2025

Publication Date

March 25, 2025

Submission Date

November 23, 2024

Acceptance Date

February 20, 2025

Published in Issue

Year 2025 Volume: 8 Number: 1

DOI

https://doi.org/10.32323/ujma.1590154

IZ

https://izlik.org/JA96JP35PA

APA

Chesneau, C. (2025). Contributions to the Fractional Hardy Integral Inequality. Universal Journal of Mathematics and Applications, 8(1), 21-29. https://doi.org/10.32323/ujma.1590154

AMA

1.Chesneau C. Contributions to the Fractional Hardy Integral Inequality. Univ. J. Math. Appl. 2025;8(1):21-29. doi:10.32323/ujma.1590154

Chicago

Chesneau, Christophe. 2025. “Contributions to the Fractional Hardy Integral Inequality”. Universal Journal of Mathematics and Applications 8 (1): 21-29. https://doi.org/10.32323/ujma.1590154.

EndNote

Chesneau C (March 1, 2025) Contributions to the Fractional Hardy Integral Inequality. Universal Journal of Mathematics and Applications 8 1 21–29.

IEEE

[1]C. Chesneau, “Contributions to the Fractional Hardy Integral Inequality”, Univ. J. Math. Appl., vol. 8, no. 1, pp. 21–29, Mar. 2025, doi: 10.32323/ujma.1590154.

ISNAD

Chesneau, Christophe. “Contributions to the Fractional Hardy Integral Inequality”. Universal Journal of Mathematics and Applications 8/1 (March 1, 2025): 21-29. https://doi.org/10.32323/ujma.1590154.

JAMA

1.Chesneau C. Contributions to the Fractional Hardy Integral Inequality. Univ. J. Math. Appl. 2025;8:21–29.

MLA

Chesneau, Christophe. “Contributions to the Fractional Hardy Integral Inequality”. Universal Journal of Mathematics and Applications, vol. 8, no. 1, Mar. 2025, pp. 21-29, doi:10.32323/ujma.1590154.

Vancouver

1.Christophe Chesneau. Contributions to the Fractional Hardy Integral Inequality. Univ. J. Math. Appl. 2025 Mar. 1;8(1):21-9. doi:10.32323/ujma.1590154