The paper is devoted to study the inversion of the integral transform ( H f ) ( x ) = ∫ 0 ∞ H p , q m , n [ x t | ( a i , α i ) 1 , p ( b j , β j ) 1 , p | ]     f ( t ) d t involving the H -function as the kernel in the space 𝔏 v , r of functions f such that ∫ 0 ∞ | t υ f ( t ) | r d t t < ∞     ( 1 < r < ∞ , ν ∈ ℝ ) .