Zhang Chao

(Department of Mathematics，Guangdong University of Education，Guangzhou 510310，China)

Products of multiplication，composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces on the unit ball

Zhang Chao

(Department of Mathematics，Guangdong University of Education，Guangzhou 510310，China)

The paper defines differentiation operator on H(B)by radial derivative，then it studies the boundedness and compactness of products of multiplication，composition and differentiation between weighted Bergman-Nevanlinna and Blochtype spaces on the unit ball.

composition operator，multiplication operator，differentiation operator，Bergman-Nevanlinna space，Bloch-type space

1 Introduction

Let D be the open unit disk in the complex plane.Let B={z∈Cn：|z|＜1}be the unit ball of Cn，and S=∂B its boundary.We will denote by dv the normalized Lebesgue measure on B.

2 MψCφR and RMψCφ

The following criterion for compactness is a useful tool to us and it follows from standard arguments，for example，to those outlined in Proposition 3.11 of[3].

3 CφRMψand RCφMψ

[1]Sharma A K.Products of multiplication，composition and differention between weighted Bergman-Nevanlinna and Bloch-tyoe spacers[J].Turk.J.Math.，2011，35(2)：275-291.

[2]Zhu Kehe.Spaces of Holomorphic Functions in the Unit Ball[M].New York：Springer-Verlag，2004.

[3]Cowen C C，MacCluer B D.Composition Operators on Spaces of Analytic Functions[M].Boca Raton：CRC Press，1995.

[4]Shapiro J H.Composition Operators and Classical Function Theory[M].New York：Springer-Verlag，1993.

[5]Hibschweiler R A，Portnoy N.Composition followed by differentiation between Bergman and Hardy spaces[J]. Rock Mountain Journal of Mathematics，2005，35(3)：843-855.

[6]Ohno S.Products of composition and differentiation between Hardy spaces[J].Bull.Austral.Math.Soc.，2006，73：235-243.

[7]Sharma A K，Sharma S D，Kumar S.Weighted composition followed by differentiation betwwen Bergman spaces[J].International Mathematical Forum.，2007，2(33)：1647-1656.

[8]Kumar S，Singh K J.Weighted composition operators on weighted Bergman spaces[J].Extracta Mathematicae，2007，22(3)：245-256.

单位球上加权Bergman-Nevanlinna空间到Bloch-型空间上乘法，复合，微分算子的乘积

张超

(广东第二师范学院数学系，广东 广州 510310)

文章用径向导数定义了H(B)空间上的微分算子，从而研究了单位球上加权Bergman-Nevanlinna空间到Bloch-型空间上乘法，复合，微分算子的乘积，给出了这类乘积有界和紧的充要条件.

符合算子；乘法算子；微分算子；Bergman-Nevanlinna空间；Bloch-type空间

O177

2015-12-21.

国家自然科学基金(11501136)；广东第二师范学院博士基金(2014ARF04).

张超(1977-)，博士，讲师，研究方向：泛函分析.

A Article ID:1008-5513(2016)03-0271-17

10.3969/j.issn.1008-5513.2016.03.006

2010 MSC:47B33，30C35，46E35