Olsen-type inequalities for the generalized commutator of multilinear fractional integrals

Authors : Xiao YU, SHANZHEN LU

Pages : 2348-2370

View : 9 | Download : 3

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we study certain multilinear operators of fractional integral type defined by \[ I^{\vec{A}}_{\alpha}\vec{f}insert ignore into journalissuearticles values(x);=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion insert ignore into journalissuearticles values(\mathbb{R} %EndExpansion ^{n});^m}\frac{f_1insert ignore into journalissuearticles values(y_1);\cdots f_minsert ignore into journalissuearticles values(y_m);}{|insert ignore into journalissuearticles values(x-y_1,\cdots,x-y_m);|^{mn-\alpha+\sum\limits_{i=1}^minsert ignore into journalissuearticles values(N_i-1);}}\prod\limits_{i=1}^mR_{N_i}insert ignore into journalissuearticles values(A_i;x,y_i);d\vec{y}, \] where $0< \alpha
Keywords : Olsen type inequality, multilinear fractional integral, generalized commutator, dyadic grids, Morrey spaces