数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (4): 561-.

• 论文 • 上一篇    下一篇

EXTENDED CES´ARO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C_{n}

 胡璋剑   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • 出版日期:2003-10-06 发布日期:2003-10-06
  • 基金资助:

    This research is partially supported by the 151 Projection
    and the Natural Science Foundation of Zhejiang Province.

EXTENDED CES´ARO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C_{n}

 HU Zhang-Jian     

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • Online:2003-10-06 Published:2003-10-06
  • Supported by:

    This research is partially supported by the 151 Projection
    and the Natural Science Foundation of Zhejiang Province.

摘要:

The paper defines an extended Ces\`{a}ro operator
$T_g$ with holomorphic  symbol $g$ in the unit ball $\bf B$ of $C^n$ as
$$
     T_g(f)(z)=\int_0^1f(tz)\Re g(tz)\frac{{\rm d}t}{t},
 \verb#       # f\in H({\bf B}),z\in \bf B. $$
Where $\Re g(z)= \sum_{j=1}^{n} z_j\fr{\partial g}
{\partial z_j}$ is  the radial
 derivative of $g$. In this paper, the author
 characterizes  $g$ for which $T_g$ is
 bounded (or compact) on the Bloch space ${\cal B}$
 and the little Bloch space ${\cal B}_0 $.

关键词: the Bloch space, extended Ces`aro operator, boundedness

Abstract:

The paper defines an extended Ces\`{a}ro operator
$T_g$ with holomorphic  symbol $g$ in the unit ball $\bf B$ of $C^n$ as
$$
     T_g(f)(z)=\int_0^1f(tz)\Re g(tz)\frac{{\rm d}t}{t},
 \verb#       # f\in H({\bf B}),z\in \bf B. $$
Where $\Re g(z)= \sum_{j=1}^{n} z_j\fr{\partial g}
{\partial z_j}$ is  the radial
 derivative of $g$. In this paper, the author
 characterizes  $g$ for which $T_g$ is
 bounded (or compact) on the Bloch space ${\cal B}$
 and the little Bloch space ${\cal B}_0 $.

Key words: the Bloch space, extended Ces`aro operator, boundedness

中图分类号: 

  • 47B38