Abstract:This paper is devoted to the study of a convolution structure denoted by $*_{\alpha}$, which is defined via the Hartley--Bessel transform. This concept was introduced in a recent work by F. Bouzeffour [\emph{J. Pseudo-Differ. Oper. Appl.}, 2024;15, Article 42]. We establish an analog of the Hausdorff--Young inequality for the Hartley--Bessel transform and convolution operator $*_{\alpha}$. This leads to the convolution $*_{\alpha}$ being uniformly bounded on the dual space. Moreover, in some special cases, our results yield a better upper bound coefficient for the convolution $*_{\alpha}$ than those previously obtained by Bouzeffour's result in [Theorem 4.4, \emph{J. Pseudo-Differ. Oper. Appl.}, 2024;15, Article 42]. Finally, we apply the convolution structure $*_{\alpha}$ to study the solvability of a particular class of integral equations and provide a priori estimates for solutions under appropriate conditions.
| Comments: | 10 pages, accepted by Integral Transforms Spec. Funct |
| Subjects: | Functional Analysis (math.FA); Classical Analysis and ODEs (math.CA) |
| MSC classes: | 42B35, 44A20, 44A35, 45E10 |
| Cite as: | arXiv:2508.02787 [math.FA] |
| (or arXiv:2508.02787v2 [math.FA] for this version) | |
| https://doi.org/10.48550/arXiv.2508.02787 arXiv-issued DOI via DataCite |
|
| Journal reference: | Integral Transforms and Special Functions. Published online: 25 May 2026 |
| Related DOI: | https://doi.org/10.1080/10652469.2026.2678565
DOI(s) linking to related resources |
From: Tuan Trinh [view email]
[v1]
Mon, 4 Aug 2025 18:01:12 UTC (11 KB)
[v2]
Tue, 26 May 2026 11:09:48 UTC (13 KB)
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