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 operators T-alpha, alpha is an element of [0, n) generated by Calderon-Zygmund operators (alpha = 0) and generated by fractional integral operator (alpha > 0) on generalized mixed Morrey spaces M-(q)over-right-arrow(phi)(R-n). Moreover, the boundeness for commutators of T-alpha, alpha is an element of [0,n) on generalized mixed Morrey spaces M-(q)over-right-arrow(phi) (R-n) is also studied. As applications, we obtain the boundedness for Hardy-Littlewood maximal operator, Calderon-Zygmund singular integral operators, fractional integral operator, fractional maximal operator and their commutators on generalzied mixed Morrey spaces.

Automated summary

This paper studies the boundedness of a large class of sublinear operators on generalized mixed Morrey spaces, including the T-alpha operators generated by Calderon-Zygmund operators and fractional integral operators, as well as their commutators. Applications to various operators such as Hardy-Littlewood maximal operator and Calderon-Zygmund singular integral operators are also discussed.