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

Abstract

In this paper, the author studies the boundedness for a large class of sublinear operator $T_{\alpha },\alpha \in [0,n)$ generated by Calder{ó}n-Zygmund operators ($\alpha =0$) and generated by fractional integral operator ($\alpha >0$) on generalized mixed Morrey spaces $M_{\vec{q}}^{\phi }({\mathbb{R}}^n)$. Moreover, the boundeness for the commutators of $T_{\alpha },\alpha \in [0,n)$ on generalized mixed Morrey spaces $M_{\vec{q}}^{\phi }({\mathbb{R}}^n)$ 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.

References in corpus (1)

• Parabolic oblique derivative problem in generalized Morrey spaces