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

Authors : Huixia MO, Dongyan YU, Huiping ZHOU

Pages : 851-861

Doi:10.3906/mat-1209-48

View : 11 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let l \in N and \vec{A}=insert ignore into journalissuearticles values(A1,\dots,Al); and \vec{f}=insert ignore into journalissuearticles values(f1,\dots,fl); be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1,\dots,fl\in Lc\inftyinsert ignore into journalissuearticles values(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}insert ignore into journalissuearticles values(\vec{f});insert ignore into journalissuearticles values(x); =\dintinsert ignore into journalissuearticles values(Rn);m \frac{\prod\limitsi=1lRmi+1insert ignore into journalissuearticles values(Ai;x,yi);fiinsert ignore into journalissuearticles values(yi);}{|insert ignore into journalissuearticles values(x-y1,\dots ,x-ym);|ln+insert ignore into journalissuearticles values(m1+m2+\dots+ml);-a} dy1\dots dyl. When DgAi\in \dot{L}biinsert ignore into journalissuearticles values(0
Keywords : Multilinear fractional integral, commutator, Triebel Lizorkin space, Lipschitz function space