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 NameAffiliation
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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Abstract:
      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 $\mathcal{B}_{\alpha,0}$.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.03.004
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