Fractional integral operators on the mixed $\lambda$-central central Morrey spaces

TL;DR

This paper introduces mixed $-central Morrey spaces and studies the boundedness of fractional integral operators and their commutators within these spaces, extending results to generalized versions.

Contribution

It defines new mixed $-central Morrey and BMO spaces and proves boundedness of fractional integral operators and commutators on these spaces, including extensions to generalized spaces.

Findings

Boundedness of $T_{}$ on mixed $$-central Morrey spaces

Boundedness of commutators $[b, T_{}]$ on these spaces

Extension of results to generalized mixed central Morrey spaces

Abstract

In this paper, the authors define the mixed $\lambda$-central Morrey spaces and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional integral operators $T_{\alpha}$ and its commutators $[b, T_{\alpha}]$ are established on the mixed $\lambda$-central Morrey spaces, respectively. Furthermore, we also extend these results to the generalized mixed central Morrey spaces.