Boundedness of certain multiple Erdélyi--Kober fractional integral operators on the Hardy space $H^1$

Abstract

In this paper, we establish the boundedness of the multiple Erdélyi--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.