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

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