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  • 标题:Finite-rank intermediate Hankel operators on the Bergman space
  • 本地全文:下载
  • 作者:Takahiko Nakazi ; Tomoko Osawa
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:2001
  • 卷号:25
  • 期号:1
  • 页码:19-31
  • DOI:10.1155/S0161171201001971
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    Let L 2 = L 2 ( D , r   d r   d θ / π ) be the Lebesgue space on the open unit disc and let L a 2 = L 2 ∩ ℋ o l ( D ) be the Bergman space. Let P be the orthogonal projection of L 2 onto L a 2 and let Q be the orthogonal projection onto L ¯ a , 0 2 = { g ∈ L 2 ; g ¯ ∈ L a 2 ,       g ( 0 ) = 0 } . Then I − P ≥ Q . The big Hankel operator and the small Hankel operator on L a 2 are defined as: for ϕ in L ∞ , H ϕ big ( f ) = ( I − P ) ( ϕ f ) and H ϕ small ( f ) = Q ( ϕ f ) ( f ∈ L a 2 ) . In this paper, the finite-rank intermediate Hankel operators between H ϕ big and H ϕ small are studied. We are working on the more general space, that is, the weighted Bergman space.

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