Commutators of multilinear strongly singular integrals on nonhomogeneous metric measure spaces

Abstract

Let (X,d,μ)\left(X,d,\mu ) denote nonhomogeneous metric measure space satisfying geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness in Lebesgue spaces for two kinds of commutators, which are iterated commutators and commutators in summation form, generated by multilinear strongly singular integral operators with RBMO(μ)\left(\mu ) function on nonhomogeneous metric measure spaces (X,d,μ)\left(X,d,\mu ) is obtained.

Keywords

• multilinear strongly singular integral
• commutators
• nonhomogeneous metric measure spaces
• rbmo(μ)
• 42b20
• 42b25