Multi-Dimensional Integral Transform with Fox Function in Kernel in Lebesgue-Type Spaces

Sergey Sitnik () and Oksana Skoromnik
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Sergey Sitnik: Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy St. 85, 308015 Belgorod, Russia
Oksana Skoromnik: Faculty of Computer Science and Electronics, Euphrosyne Polotskaya State University of Polotsk, Blokhin St. 29, 211440 Novopolotsk, Belarus

Mathematics, 2024, vol. 12, issue 12, 1-10

Abstract: This paper is devoted to the study of the multi-dimensional integral transform with the Fox H -function in the kernel in weighted spaces with integrable functions in the domain R + n with positive coordinates. Due to the generality of the Fox H -function, many special integral transforms have the form studied in this paper, including operators with such kernels as generalized hypergeometric functions, classical hypergeometric functions, Bessel and modified Bessel functions and so on. Moreover, most important fractional integral operators, such as the Riemann–Liouville type, are covered by the class under consideration. The mapping properties in Lebesgue-weighted spaces, such as the boundedness, the range and the representations of the considered transformation, are established. In special cases, it is applied to the specific integral transforms mentioned above. We use a modern technique based on the extensive use of the Mellin transform and its properties. Moreover, we generalize our own previous results from the one-dimensional case to the multi-dimensional one. The multi-dimensional case is more complex and needs more delicate techniques.

Keywords: multi-dimensional integral transform; Fox H -function; Melling transform; weighted space; fractional integrals and derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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