Multi-Dimensional Generalized Integral Transform in the Weighted Spaces of Summable Functions

Abstract

In this paper, we study a multi-dimensional generalized integral transformation. The functional and compositional properties of the integral transformation in spaces of summable functions are investigated. The scheme of study is similar to the process of constructing the theory of the H-transformation, in which the central place is given to the questions of bounded and oneto-one action of the corresponding integral operator in spaces of integrable functions with weight concentrated at zero and at infinity. Theory of the considered integral transformation in weighted spaces of summable functions is constructed.

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

“…To formulate the results for the transform H f (1), we need the following constants ( [1]), which are analogous for the one-dimensional case defined via the parameters of the H-function Let α = ( α 1 , α 2 , . .…”

“…Our paper is devoted to the study of the H-transform (1) in Lebesgue-type weighted spaces L ν, 2 of functions f In this paper, we apply some our previous results to obtain mapping properties such as the boundedness, the range and the representations for the H-transform (1).…”

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

“…In this paper we apply the results from [2] to obtain mapping properties such as boundedness, the rang and representations for the H-transform (1).…”

Adapting a new formula to generalize multidimensional transforms

“…Therefore, researchers who study applications and properties of integral transforms of the same category can achieve their goals directly depending on this research. For readers who are interested in multidimensional integral transforms, they can refer to other studies [30, 31].…”