Banach型函数空间包含了经典的Lp空间、变指数空间、Lorentz空间以及Orlicz空间等一系列调和分析中的重要函数空间。本项目力争将调和分析中一些现有结论推广至此类函数空间。我们拟开展如下研究问题：.1.几类积分算子在Banach函数空间与Banach型Morrey空间中的加权估计。.2.通过积分算子在不同的Banach型函数空间中有界的必要性刻画BMO、Lipschitz和Campanato这三类空间；交换子在Banach函数空间中的有界性；几类积分算子在由Banach函数空间生成的新型函数空间中的有界性。.3.重排不变拟Banach函数空间包含了Lp(p>0)空间。积分算子在此类空间中的紧性问题和在此类空间中的外插定理以及调和分析中的若干重要不等式在此类空间中是否还成立是本项目要考虑的第三方面问题。

Banach type function space includes the classical Lp space、 variable exponent space、 Lorentz space and Orlicz space. This project tries to extend the known results of harmonic analysis to such function spaces. We plan to study the following questions..1. The weighted estimates for several kinds of integral operators on Banach function space and Banach type Morrey space..2. The characterization of BMO、Lipschitz and Campanato spaces via the necessarity of the boundedness of integral operators on various Banach type function spaces. The boundedness of commutators on Banach function spaces and the boundedness for several kinds of integral operators on new type function spaces generated by the Banach function space..3. Rearrangement-invariant quasi Banach function space includes the Lp(p>0) space. The third question of this project is to study the compactness of integral operators on such function space, the extrapolation theorem of integral operators on such function space and some important ineuqualities of harmonic analysis on such function space.