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

Let l \in N and \vec{A}=(A1,\dots,Al) and \vec{f}=(f1,\dots,fl) be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1,\dots,fl\in Lc\infty(Rn). Let x\notin\capi=1lSupp fi. The generalized higher commutator generated by the multilinear fractional integral is then given by Ia,m\vec{A}(\vec{f})(x) =\dint(Rn)m \frac{\prod\limitsi=1lRmi+1(Ai;x,yi)fi(yi)}{|(x-y1,\dots ,x-ym)|ln+(m1+m2+\dots+ml)-a} dy1\dots dyl. When DgAi\in \dot{L}bi(0

Anahtar Kelimeler:

Multilinear fractional integral, commutator, Triebel--Lizorkin space, Lipschitz function space

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

Keywords:

Multilinear fractional integral, commutator, Triebel--Lizorkin space, Lipschitz function space,

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