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Start Over Author "Zhangjian Hu" Journal proceedings of the american mathematical society
5 results on '"Zhangjian Hu"'

3. Extended Cesàro operators on mixed norm spaces

Author

Zhangjian Hu

Subjects
Combinatorics, Unit sphere, Operator (computer programming), Mixed norm, Applied Mathematics, General Mathematics, Bounded function, Mathematical analysis, Holomorphic function, Radial derivative, Space (mathematics), Mathematics
Abstract

We define an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of C n as T g (f)(z) = ∫ 1 0 f(tz)R g (tz)dt/t, f ∈ H(B), z ∈ B, where R g (z) = Σ n j=1 z j ∂ f /∂ zj 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 (ω).

Published
2002

4. Schatten(-Herz) class extended Cesàro operators on Bergman spaces in the unit ball of ${\mathbf {C}}^n$

Author

Zhangjian Hu and Xiaomin Tang

Subjects
Unit sphere, Large class, Pure mathematics, Class (set theory), Bergman space, Applied Mathematics, General Mathematics, Mathematical analysis, Holomorphic function, Schatten class operator, Mathematics, Bergman kernel
Abstract

For a large class of weights ϕ, we characterize the holomorphic symbols g, for which the extended Cesaro operators Tg acting on the weighted Bergman space A 2 ϕ (B) are in the Schatten (or Schatten-Herz) class in the unit ball of C n .

Published
2010

5. Extended Cesàro operators on mixed norm spaces.

Author

Zhangjian Hu

Subjects
ALGEBRAIC spaces, HOLOMORPHIC functions
Abstract

We define an extended Cesàro operator $T_g$ with holomorphic symbol $g$ in the unit ball $B$ of $C^n$ as \[ T_g(f)(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}, \qquad f\in H(B),z\in B, ] where $\Re g(z)= \sum_{j=1}^{n} z_j\fr{\partial f}{\partial z_j}$ 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 $H_{p,q}(w)$. [ABSTRACT FROM AUTHOR]

Published
2003
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