摘要
Blog(α,β)空间和Qk(p,q)空间的提出使得函数空间理论研究的范围进一步扩大,所获得的结果也更加广泛,这无论对该方向的发展还是对其他一些相关领域的研究都有很大的推动作用。本文主要从以下三个方面对这两个空间的性质进行了研究,得出的主要结果均推广了已有的一些结论。
首先,讨论了单位圆上对数(α,β)-Bloch空间的基本性态,其中包括对数(α,β)-Bloch空间的积分性质,以及小对数(α,β)-Bloch空间的相应积分性质,并利用Carleson测度对对数(α,β)-Bloch进行了等价刻画.
其次,讨论了对数(α,β)-Bloch空间上的复合算子Cψ的有界性和紧性.
最后,研究了从不同的Bloch型空间Bα、Blogα。到Qk(p,q)空间的加权复合算子算子的有界性问题,并给出了算子是有界的充要条件.
The introduction of Blog,(α,β) and Qk (p.q) spaces enlarge the scope of the research of function space theory. The conclusions obtained are more extensive. This would give enormous impetus both to the development of this direction and to the research of some other related fields. In this paper, we mainly make a research on the properties of these two spaces from the following three aspects, and obtain the key results, which extends some known results.
First, we discuss some basic properties of Blog(α,β) spaces on the unit disc, including integral properties of logarithmic (α,β)-Bloch spaces、corresponding integral properties of little logarithmic (α,β)-Bloch spaces and using Carless measure to charactering logarithmic(α,β)-Bloch spaces.
Second, we characterize the boundedness and compactness of composition operators Cφon Blog(α,β) spaces.
At last, we investigate the boundedness of weighted composition operators acting from different Bloch type spaces such as Bαspaces、Blogαspaces to QK(p,q) spaces, and give the necessary and sufficient condition.
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