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.

單位球上加權(quán)Bergman-Nevanlinna空間到Bloch-型空間上乘法，復(fù)合，微分算子的乘積

張超

(廣東第二師范學(xué)院數(shù)學(xué)系，廣東 廣州 510310)

文章用徑向?qū)?shù)定義了H(B)空間上的微分算子，從而研究了單位球上加權(quán)Bergman-Nevanlinna空間到Bloch-型空間上乘法，復(fù)合，微分算子的乘積，給出了這類乘積有界和緊的充要條件.

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

O177

2015-12-21.

國(guó)家自然科學(xué)基金(11501136)；廣東第二師范學(xué)院博士基金(2014ARF04).

張超(1977-)，博士，講師，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