论文标题
广泛的积分类型希尔伯特操作员作用于加权蓝路空间
Generalized integral type Hilbert operator acting on weighted Bloch space
论文作者
论文摘要
令$μ$为$ [0,1）$的有限鲍勒度量。在本文中，我们考虑了普遍的整体类型希尔伯特操作员 $$ \ MATHCAL {I} _ {μ_{μ_{α+1}}（f）（z）= \ int_ {0}^{1}^{1} \ frac {f（t）} {（1-TZ）^{1-TZ）^{α+1}}dμ（t） $ \ mathcal {i} _ {μ_{1}} $最近已被广泛研究。本文的目的是研究$ \ mathcal {i} _ {μ_{μ_{α+1}} $从正常重量Bloch空间起作用的界限（分别紧凑）_ {μ_{μ_{μ_{α+1}} $。作为我们研究的后果，我们完全获得了$ \ Mathcal {i} _ {μ_{μ_{α+1}} $在Bloch类型空间，对数BLOCH空间之间作用的界限。
Let $μ$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\mathcal{I}_{μ_{α+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{α+1}}dμ(t)\ \ \ (α>-1).$$ The operator $\mathcal{I}_{μ_{1}}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of $\mathcal{I}_{μ_{α+1}}$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of $ \mathcal{I}_{μ_{α+1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others.
