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On inversion of $$H$$-transform in $${\mathfrak L}_{v,r}$$-space. (English) Zbl 0912.33005
This paper deals with the inversion of an integral transform of a function $$f$$ when the kernel is a general $$H$$-function and when $$f$$ satisfies the condition $\int^\infty_0 \bigl| t^\nu f(t)\bigr|^r {dt\over t} <\infty,\;1<r< \infty,\;\nu\text{ real}.$ Inversion theorems are obtained for various situations involving the parameters. The main results are entensions of the corresponding results when the kernel is a $$G$$-function, obtained by P. G. Rooney [Proc. R. Soc. Edinb. Sect. A 93, 265-297 (1983; Zbl 0509.44001)].

##### MSC:
 33C60 Hypergeometric integrals and functions defined by them ($$E$$, $$G$$, $$H$$ and $$I$$ functions) 44A20 Integral transforms of special functions
##### Keywords:
$$G$$-function
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