Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions

Abstract

Let l ∈ N and ⃗ A = (A1, . . . , A l ) and ⃗ f = (f1, . . . , f l ) be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1, . .Suppfi. The generalized higher commutator generated by the multilinear fractional integral is then given bythe authors establish the boundedness of I ⃗ A α,m on the product Lebesgue space, Triebel-Lizorkin space, and Lipschitz space.

Olsen-type inequalities for the generalized commutator of multilinear fractional integrals

“…The commutator theory for the multilinear fractional integral operators can be found in [5,44], among others. Recently, Mo et al [28] studied the following generalized commutator of the multilinear fractional integral defined by…”

Boundedness of commutators generated by m-th Calderón-Zygmund type singular integrals and local Campanato functions on generalized local Morrey spaces

“…In recent years, the multilinear singular integrals have been attracting attention and great developments have been achieved (see [1][2][3][4][5][6][7][8][9][10][11]). The study for the multilinear singular integrals is motivated not only by a mere quest to generalize the theory of linear operators but also by their natural appearance in analysis.…”