Musielak-Orlicz Herz空间上的块分解及其应用

The Block Decomposition of Musielak-Orlicz Herz Spaces and Its Applications

函数空间及其相关理论一直是本科阶段泛函分析课程的重要内容.聚焦函数空间块分解性质这一个问题的研究是因为函数空间上的一些算子有界性问题可归结为这些算子在该空间块上的一致有界性估计问题.为充分展示这一核心思想,我们先证明了Musielak-Orlicz Herz空间上的块分解定理,再利用该定理给出了一类奇异积分算子在齐次Musielak-Orlicz Herz空间中有界性的新证明.

Function spaces and their related theories are important in the course of functional analysis.One of the interesting problems is the block decomposition of function spaces.It is because of that the boundedness of some classical operators on function spaces can be reduced to the uniform boundedness of these operators on corresponding blocks of the spaces.In the article,we present a block decomposition theorem for Musielak-Orlicz Herz spaces.As an application of the theorem,we offer a novel proof of the boundedness of a class of singular integral operators in homogeneous Musielak-Orlicz Herz spaces.