Products of multiplication, composition and differentiation on weighted Bergman spaces in the unit ball

ZHANG Chao; QIN Yuehai

doi:10.13471/j.cnki.acta.snus.ZR20240184

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Products of multiplication, composition and differentiation on weighted Bergman spaces in the unit ball

Research articles | 更新时间：2025-11-14

- Products of multiplication, composition and differentiation on weighted Bergman spaces in the unit ball
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 2, Pages: 160-169(2025)
- 作者机构：
  
  广东第二师范学院数学系, 广东广州 510310
- 作者简介：
  
  ZHANG Chao E-mail：zhangchaomhw2003@126.com
  QIN Yuehai E-mail：haiqy2000@gdei.edu.cn
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240184
  CLC： O177.2
- Received：01 June 2024，
  
  Accepted：10 July 2024，
  
  Published Online：25 July 2024，
  
  Published：15 March 2025
- 稿件说明：
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张超,覃跃海.单位球上加权Bergman空间上乘法、复合与微分算子的乘积[J].中山大学学报(自然科学版)(中英文),2025,64(02):160-169.

ZHANG Chao,QIN Yuehai.Products of multiplication, composition and differentiation on weighted Bergman spaces in the unit ball[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(02):160-169.
张超,覃跃海.单位球上加权Bergman空间上乘法、复合与微分算子的乘积[J].中山大学学报(自然科学版)(中英文),2025,64(02):160-169. DOI： 10.13471/j.cnki.acta.snus.ZR20240184.

ZHANG Chao,QIN Yuehai.Products of multiplication, composition and differentiation on weighted Bergman spaces in the unit ball[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(02):160-169. DOI： 10.13471/j.cnki.acta.snus.ZR20240184.

摘要

研究了单位球上加权Bergman空间上乘法、复合与微分算子的乘积的有界性和紧性. 通过径向导数，我们定义了单位球上解析函数空间上的微分算子，从而推广了Sharma的结果.

Abstract

The boundness and compactness of products of multiplication

composition and differentiation on weighted Bergman spaces in the unit ball are studied. We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative. Then we extend the Sharma's results.

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references

COWEN C C ， MACCLUER B D ， 1995 . Composition operators on spaces of analytic function ［M］. Boca Raton ： CRC Press .

HIBSCHWEILER R A ， PORTNOY N ， 2005 . Composition followed by differentiation between Bergman and Hardy space ［J］. Rocky Mountain J Math ， 35 （ 3 ）： 843 - 855 .

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SHAPIRO J H ， 1993 . Composition operators and classical function theory ［M］. New York ： Springer .

SHARMA A K ， 2011 . Products of multiplication， composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces ［J］. Turk J Math ， 35 （ 2 ）： 275 - 291 .

SHARMA A K ， SHARMA S D ， KUMAR S ， 2007 . Weighted composition followed by differentiation between Bergman spaces ［J］. Int Math Forum ， 2（33/34/ 35 / 36 ）： 1647 - 1656 .

ZHAO R H ， ZHU K H ， 2006 . Theory of Bergman spaces in the unit ball of <math id="M470"><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=75520862&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=75520823&type= 2.96333337 2.53999996 ［EB/OL］. arXiv ： math/ 0611093 . https://arxiv.org/abs/math/0611093 https://arxiv.org/abs/math/0611093 .

ZHU K H ， 2004 . Spaces of holomorphic functions in the unit ball ［M］. New York ： Springer .

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