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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Extended Cesàro operators on mixed norm spaces


Author: Zhangjian Hu
Journal: Proc. Amer. Math. Soc. 131 (2003), 2171-2179
MSC (2000): Primary 47B38, 32A36
Published electronically: December 30, 2002
MathSciNet review: 1963765
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Abstract: We define an extended Cesàro operator $T_g$ with holomorphic symbol $g$ in the unit ball $B$ of $C^n$ as

\begin{displaymath}T_g(f)(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}, \qquad f\in H(B),z\in B, \end{displaymath}

where $\Re g(z)= \sum_{j=1}^{n} z_j\frac{\partial f}{\partial z_j}$ is the radial derivative of $g$. In this paper we characterize those $g$ for which $T_g$ is bounded (or compact) on the mixed norm space $H_{p,q}(w)$.


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Additional Information

Zhangjian Hu
Affiliation: Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang, 313000, People’s Republic of China — and — Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599
Email: huzj@mail.huptt.zj.cn, huz@email.unc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06777-1
PII: S 0002-9939(02)06777-1
Keywords: Ces\`{a}ro operator, mixed norm space, normal weight
Received by editor(s): May 8, 2001
Received by editor(s) in revised form: February 26, 2002
Published electronically: December 30, 2002
Additional Notes: This research was partially supported by the 151 Projection and the Natural Science Foundation of Zhejiang Province
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society