On inversion of H-Transform in $\eufb114_{\nu ,r}$-space

Abstract

The paper is devoted to study the inversion of the integral transform $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,\alpha_i)_{1,p}\\[1mm](b_j,\beta_j)_{1,q} \end{array}\right.\right]f(t)dt$$ involving the $H$-function as the kernel in the space $\euf114_{\nu ,r}$ of functions $f$ such that $$\int^\infty_0\left|t^\nu f(t)\right|^r\frac{dt}t<\infty\quad(1<r<\infty, \ \nu\in\msb122).$$