Bloch型空间上一个积分算子的有界性

Boundedness of an Integral Operator on Bloch-Type Spaces

中文关键词:  有界性  积分算子  Bloch型空间  Hardy空间

英文关键词:Boundedness  integral operator  Bloch-type space  Hardy space

中文摘要:

      本文研究了单位圆盘$\mathbb{D}$上的一个积分算子,定义如下$Kf(z)=\int_{\mathbb{D}}\frac{f(w)}{1-z\bar{w}}{\rm d}A(w)$, 该算子可以看作经典Bergman投影的姐妹算子,同时我们得到了该算子关于Bloch型空间, $H^{\infty}$空间以及$L^{p}$空间之间有界的充分必要条件.

英文摘要:

      In this paper, we study the boundedness of an integral operator $K$ over the unit disk $\dd$, defined as $Kf(z)=\int_{\dd}\frac{f(w)}{1-z\bar{w}}\d A(w)$, which can be viewed as a cousin of the classical Bergman projection, and we establish satisfactory boundedness results between Bloch-type spaces, $H^{\infty}$ and $L^{p}$ spaces.