Chinese Quarterly Journal of Mathematics ›› 2004, Vol. 19 ›› Issue (4): 331-337.

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The Spaces bp with 0 < p < 1

  

  1. 1.Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; 2.Department of Mathematics, Huzhou Teacher's College, Huzhou 313000, China
  • Received:2004-08-12 Online:2004-12-30 Published:2024-02-28
  • About author:HU Zhang-jian(1957-),male,native of Tongxiang,Zhejiang,a professor of Huzhou Teacher's College,engages in function theory and operator theory;LIU Tai-shun(1957-),male,native if Huoshan,Anhui, a professor of University of Science and Technology of China,engages in SCV.
  • Supported by:
     SupportedinPartbythe151Projection(971019) SupportedbytheNaturalScienceFoundationofZhejiangProvince(M103104);

Abstract: Let 0 < p < 1. In this paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = Rn-1 × R+ is the upper half space. As an application, we get the boundedness of harmonic conjugation operators on bp(H).

Key words: Bergman space, upper half space, harmonic conjugation

CLC Number: