Characterizations for the boundedness of multi-sublinear operators and their commutators on three kinds of generalized weighted Morrey spaces and applications

Xi Cen, Xiang Li, Dunyan Yan

Published 2023-05-22Version 1

The main questions raised in this paper are to find the sufficient conditions that make multi-sublinear operators $T$ and their commutators ${T_{\prod \vec b }}$, ${T_{\sum {\vec b} }}$ to be bounded on three kinds of generalized weighted Morrey spaces. In subsection 1.2, we give the main theorems of this paper to solve the above related questions. As corollaries of the main theorems, we give sufficient and necessary conditions for a class of multi-sublinear operators which are bounded on three kinds of generalized weighted Morrey spaces. In subsection 1.3, we give the boundedness of $m$-linear Littlewood-Paley square operators and their commutators, commutators of bilinear pseudo-differential operators with mild regularity and commutators of Paraproducts with mild regularity as applications of the main theorems.