Boundedness of certain multiple Erd\'{e}lyi-Kober fractional integral operators on the Hardy space $H^1$

TL;DR

This paper proves the boundedness of multiple Erdélyi-Kober fractional integral operators involving Fox's H-function on the Hardy space H^1, extending recent results and exploring connections to Hausdorff operators.

Contribution

It establishes the boundedness of these fractional integral operators on H^1, generalizing prior work and linking to Hausdorff operators.

Findings

Boundedness of Erdélyi-Kober operators on H^1 established

Generalization of previous boundedness results

Connections to Hausdorff operators discussed

Abstract

In this paper, we establish the boundedness of the multiple Erd\'{e}lyi-Kober fractional integral operators involving Fox's $H$-function on the Hardy space $H^1$. Our results generalize recent results of Kwok-Pun Ho [Proyecciones 39 (3) (2020), 663--677]. Some useful connections related to the Hausdorff operators are also mentioned.