Olsen-type inequalities for the generalized commutator of multilinear fractional integrals
Authors: XIAO YU, SHANZHEN LU
Abstract:
In this paper, we study certain multilinear operators of
fractional integral type defined by
\[
I^{\vec{A}}_{\alpha}\vec{f}(x)=\int_{%
%TCIMACRO{\U{211d} }%
%BeginExpansion
(\mathbb{R}
%EndExpansion
^{n})^m}\frac{f_1(y_1)\cdots f_m(y_m)}{|(x-y_1,\cdots,x-y_m)|^{mn-\alpha+\sum\limits_{i=1}^m(N_i-1)}}\prod\limits_{i=1}^mR_{N_i}(A_i;x,y_i)d\vec{y},
\]
where $0< \alpha
Keywords:
Olsen-type inequality, multilinear fractional integral, generalized commutator, dyadic grids, Morrey spaces
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