BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES

Abstract

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