  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
  $$\int^\infty_0\left|t^\nu f(t)\right|^r\frac{dt}t<\infty\quad(1<r<\infty, \
\nu\in\msb122).$$
