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 [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
Nearby in the stack
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, 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.
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