Abstract
Let T_{Pivec {b}} be the commutator generated by a multilinear square function and Lipschitz functions with kernel satisfying Dini-type condition. We show that T_{Pivec {b}} is bounded from product Lebesgue spaces into Lebesgue spaces, Lipschitz spaces, and Triebel–Lizorkin spaces.
Highlights
We give the definition of the multilinear square function of type ω(t)
Let A(x) be an elliptic n × n matrix with complex-valued entries that are merely bounded and measurable, and let T = div(A(x)∇)
Fabes et al [6] studied a family of multilinear square functions and applied it to the Kato problem. They obtained a collection of multilinear Littlewood–Paley estimates and applied them to two problems in partial differential equations
Summary
We give the definition of the multilinear square function of type ω(t). Cc∞(Rn), we say is a multilinear square function of type ω(t) if Qm Remark 1.1 When ω(x) = xγ for some γ > 0, the boundedness of a multilinear square function was studied by Xue et al [18]. Bm), the iterated commutator of a multilinear square function is defined by
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