New Multilinear Littlewood–Paley g_λ^* Function and Commutator on weighted Lebesgue Spaces

Via the new weight function A_p⃗^θ(φ ), the authors introduce a new class of multilinear Littlewood–Paley g_λ^* 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_λ^* function and the new BMO function on weighted Lebesgue spaces. The results in this article include the known results in . When m=1, that is, in the case of one-linear, our conclusions are also new, further extending the results in .