The Norm of a Class of Singular Integral Operators from $L^{\infty}$ onto Bloch-Type Spaces
Received:March 21, 2017  Revised:March 01, 2018
Key Word: operator norm   singular integral operator   Bloch-type space
Fund ProjectL:Supported by the Natural Science Foundation of Zhejiang Province (Grant No.LY14A010021).
 Author Name Affiliation Xiaoyang HOU Basic Department, Wenzhou Business College, Zhejiang 325035, P. R. China Department of Mathematics, Wenzhou University, Zhejiang 325035, P. R. China Yi XU Department of Mathematics, Wenzhou University, Zhejiang 325035, P. R. China
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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 $\mathcal{B}_{\alpha,0}$.