Upper bound coefficient for convolution structure associated to Hartley--Bessel transform
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914603555880960 |
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| author | Tuan, Trinh |
| author_facet | Tuan, Trinh |
| contents | This paper is devoted to the study of a convolution structure denoted by $*_α$, 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 $*_α$. This leads to the convolution $*_α$ being uniformly bounded on the dual space. Moreover, in some special cases, our results yield a better upper bound coefficient for the convolution $*_α$ 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 $*_α$ to study the solvability of a particular class of integral equations and provide a priori estimates for solutions under appropriate conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper bound coefficient for convolution structure associated to Hartley--Bessel transform Tuan, Trinh Functional Analysis Classical Analysis and ODEs 42B35, 44A20, 44A35, 45E10 This paper is devoted to the study of a convolution structure denoted by $*_α$, 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 $*_α$. This leads to the convolution $*_α$ being uniformly bounded on the dual space. Moreover, in some special cases, our results yield a better upper bound coefficient for the convolution $*_α$ 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 $*_α$ to study the solvability of a particular class of integral equations and provide a priori estimates for solutions under appropriate conditions. |
| title | Upper bound coefficient for convolution structure associated to Hartley--Bessel transform |
| topic | Functional Analysis Classical Analysis and ODEs 42B35, 44A20, 44A35, 45E10 |
| url | https://arxiv.org/abs/2508.02787 |