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ABSTRACT. The paper is devoted to study the inversion of the integral transform (Hf)(x) fo H,' [xt (a"a')l" f(t)dt involving the H-function as the kernel in the space ,, of functions jr such that fo itf(t)l dt -

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.