New multilinear Littlewood–Paley gλ∗ function and commutator on weighted Lebesgue spaces

Via the new weight function , the authors introduce a new class of multilinear Littlewood–Paley 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 function and the new function on weighted Lebesgue spaces. The results in this article include the known results in previous studies. When , that is, in the case of one linear, our conclusions are also new, further extending the results in previous work.