Boundedness criterion for sublinear operators and commutators on generalized mixed Morrey spaces

Mingquan Wei

Published 2021-06-24Version 1

In this paper, the author studies the boundedness for a large class of sublinear operator $T_\alpha, \alpha\in[0,n)$ generated by Calder{\'o}n-Zygmund singular integral operators ($\alpha=0$) and generated by fractional integral potential operators ($\alpha>0$) on the generalized mixed Morrey spaces $M^\varphi_{\vec{q}}(\Bbb R^n)$. Moreover, the boundeness for the commutators of $T_\alpha, \alpha\in[0,n)$ on the generalized mixed Morrey spaces $M^\varphi_{\vec{q}}(\Bbb R^n)$ is also studied. As applications, we obtain the boundedness for the Hardy-Littlewood maximal operator, the Calder{\'o}n-Zygmund singular integral operator, the fractional integral operator, the fractional maximal operator and their commutators on the generalzied mixed Morrey spaces.