双线性分数次积分算子及其交换子在Morrey空间中的加权估计

Weighted estimates for bilinear fractional integral operators and their commutators on Morrey spaces

本文考虑如下形式的双线性分数次积分算子:■,研究它的一般交换子在Morrey空间中的双权估计.本文证明了这些算子的一个极大函数控制定理,即当权属于A∞时,这些算子的加权Morrey范数可以被一种自然的极大算子的加权Morrey范数来控制.作为定理的推论,本文得到双线性形式的Olsen不等式、Fefferman-Stein型对偶不等式以及与双线性Hilbert变换相关的双线性极大函数的新的加权估计.作为重要的应用,本文建立双线性版本的Stein-Weiss分数次积分不等式.

This paper is devoted to proving a plethora of weighted estimates on Morrey spaces for bilinear fractional integral operators and their general commutators with bounded mean oscillation functions of the form■.We also prove some maximal function control theorems for these operators,i.e.,the weighted Morrey norm is bounded by the weighted Morrey norm of a natural maximal operator when the weight belongs to A∞.As a corollary,some new weighted estimates for the bilinear maximal function associated with the bilinear Hilbert transform are obtained.Furthermore,we formulate a bilinear version of Stein-Weiss inequality on Morrey spaces for fractional integrals,which has its own interests.