journal6 ›› 2003, Vol. 24 ›› Issue (1): 5-8.

• 数学 • 上一篇    下一篇

Cn中Stieltjes积分族与几个全纯函数空间的关系

  

  1. (湖南师范大学数学与计算机科学学院,湖南 长沙 410006)
  • 出版日期:2003-03-15 发布日期:2012-11-09
  • 作者简介:赵茜(1979-),女,湖南省湘潭市人,湖南师范大学硕士研究生,主要从事函数论研究.
  • 基金资助:

    国家自然科学基金资助项目(19871026)

Relations of Families of Stieltjes Integrals and Several Holomorphic Function Spaces on Cn

  1. (College of Mathematics and Computer Science,Hunan Normal University,Changsha 410006,Hunan China)
  • Online:2003-03-15 Published:2012-11-09

摘要:在Cn中讨论了Cauchy-Stieltjes积分族Jp和Bloch型空间、Besov空间、Bergman空间的包含关系,得到如下结果:(1)当0≤q<p+1-n时,βqJp;(2)当p≥0,q>p+1时,Jpβq;(3)当q>p≥0时,JpΔq;(4)当p>0时,ΔpJp;(5)当0<p<n+1且0<q<(n+1)/p时,JpLqa;(6)当n+1<p<∞且max{0,n+1-(pn)/(n+1)}<σ<1时,L(n+1)/p)aJp+σ.

关键词: Stieltjes积分族, Bloch型空间, Besov空间, Bergman空间, 包含

Abstract: The relations of inclusion are studied between families of Stieltjes integrals and Bloch type space,Besov space,Bergman space on Cn.The following results are obtained:(1)If 0≤q<p+1-n then βqJp;(2)If p≥0,q>p+1 then Jpβq;(3)If q>p≥0 then JpΔq;(4)If p>0 then ΔpJp;(5)If 0<p<n+1 and 0<q<(n+1)/p then JpLqa;(6)If n+1<p<∞ and max{0,n+1-(pn)/(n+1)}<σ<1 then L(n+1)/paJp+σ.

Key words: families of Stieltjes intergrals, Bloch type space, Besov space, Bergman space, inclusion

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