Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 5
Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions
- Pages
- 851–861
- DOI
- —
Abstract
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
Özet
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