从$L^{\infty}$空间到Bloch型空间一类奇异积分算子的范数

The Norm of a Class of Singular Integral Operators from $L^{\infty}$ onto Bloch-Type Spaces

中文关键词:  算子范数  奇异积分算子  Bloch型空间

英文关键词:operator norm  singular integral operator  Bloch-type space

中文摘要:

      本文研究了单位圆盘上从$L^{\infty}(\mathbb{D})$空间到Bloch型空间 $\mathcal{B}_\alpha$ 一类奇异积分算子$Q_\alpha, \alpha>0$的范数, 该算子可以看成投影算子$P$ 的推广，定义如下$$Q_\alpha f(z)=\alpha \int_{\mathbb{D}}\frac{f(w)}{(1-z\bar{w})^{\alpha+1}}\d A(w),$$ 同时我们也得到了该算子从 $C(\overline{\mathbb{D}})$空间到小Bloch型空间$\mathcal{B}_{\alpha,0}$上的范数.

英文摘要:

      In this paper, we obtain the exact norm of a class of singular i/ntegral operators $Q_\alpha, \alpha>0$, defined by $$Q_\alpha f(z)=\alpha \int_{\mathbb{D}}\frac{f(w)}{(1-z\bar{w})^{\alpha+1}}\d A(w),$$ from $L^{\infty}(\mathbb{D})$ onto Bloch-type space $\mathcal{B}_\alpha$ over the unit disk $\mathbb{D}$, which is an extension of the Bergman projection $P$. We also consider the norm for this operator from $C(\overline{\mathbb{D}})$ onto the little Bloch-type space $\mathcal{B}_{\alpha,0}$.