The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces IV

TL;DR

This paper extends the analysis of the Riemann-Liouville fractional integral in Bochner-Lebesgue spaces, focusing on boundedness for new parameter ranges and exploring its behavior in non-standard function spaces.

Contribution

It provides new boundedness results for the fractional integral when lpha > 1/p and extends the analysis to non-standard function spaces.

Findings

Boundedness established for lpha > 1/p

Extended results to non-standard function spaces

Comprehensive summary of fractional integral properties

Abstract

In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order $\alpha > 0$ in Bochner-Lebesgue spaces. We specifically address the remaining cases concerning its boundedness when $\alpha > 1/p$. Furthermore, we extend some of our previous results by investigating some non-standard function spaces. Finally, we provide a comprehensive summary of the obtained results.