Wang Hua
College of Mathematics and Econometrics, Hunan University, Changsha, 410082 P.R. China.
J Inequal Appl. 2017;2017(1):6. doi: 10.1186/s13660-016-1279-6. Epub 2017 Jan 3.
In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators [Formula: see text] in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [Formula: see text] formed by and [Formula: see text] are established. Also we study related problems about two-weight, weak type inequalities for [Formula: see text] and [Formula: see text] in the Morrey-type spaces and give partial results.
在本文中，我们首先引入一些新的莫雷型空间，其中广义莫雷空间和具有两个权重的加权莫雷空间作为特殊情况包含在内。然后我们给出这些新的莫雷型空间中分数次积分算子[公式：见原文]的加权强型和弱型估计。此外，还建立了由[公式：见原文]和[公式：见原文]构成的线性交换子[公式：见原文]的加权强型估计和端点估计。我们还研究了莫雷型空间中关于[公式：见原文]和[公式：见原文]的双权重弱型不等式的相关问题，并给出了部分结果。
