New Multilinear Littlewood--Paley g_^* Function and Commutator on weighted Lebesgue Spaces with New Weight

Via the new weight function A ₏^ (), the authors introduce a new class of multilinear Littlewood--Paley g_^* functions and establish the boundedness on weighted Lebesgue spaces. In addition, the authors obtain the boundedness of the multilinear commutator and multilinear iterated commutator generated by the multilinear Littlewood--Paley g_^* function and the new BMO function on weighted Lebesgue spaces. The results in this article include the known results in XY2015, SXY2014. When m=1, that is, in the case of one-linear, our conclusions are also new, further extending the results in S1961.