L^p-bounded operators involving generalized hypergeometric functions

Abstract

We herein determine an integral representation of generalized hypergeometric functions _m F _m extending the usual results on ₁ F ₁. After formulating integral operators involving the generalized hypergeometric functions of the form:

and

we prove that these operators are composition of generalized variants of the Laplace transform (and Watson) and Erdelyi–Kober fractional integral operators. We also prove that these operators are bounded in L ^p .

Keywords:

• fractional integral transforms
• Liouville and Kober fractional integrals
• generalized hypergeometric functions
• integral transforms with generalized hypergeometric functions in the kernel

AMS Subject Classification :

• 44A15
• 26A33
• 26A09
• 33C05
• 33C20

Acknowledgements

The authors would like to express profound gratitude to Prof. H.M. Srivastava for deeper review of this paper and his valuable advice and the referee's useful suggestions that led to an improved presentation of the paper.