Abstract
In this paper, we study the boundedness for a large class of multi-sublinear operators T m generated by multilinear Calderón-Zygmund operators and their commutators T m , i b ( i = 1 , … , m ) on the product generalized mixed Morrey spaces M q 1 → φ 1 ( R n ) × ⋯ × M q m → φ m ( R n ) . We find the sufficient conditions on ( φ 1 , … , φ m , φ ) which ensure the boundedness of the operator T m from M q 1 → φ 1 ( R n ) × ⋯ × M q m → φ m ( R n ) to M q → φ ( R n ) . Moreover, the sufficient conditions for the boundeness of T m , i b from M q 1 → φ 1 ( R n ) × ⋯ × M q m → φ m ( R n ) to M q → φ ( R n ) are also studied. As applications, we obtain the boundedness for the multi-sublinear maximal operator, the multilinear Calderón-Zygmund operator and their commutators on product generalzied mixed Morrey spaces.
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