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Finite-rank intermediate Hankel operators on the Bergman space

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  • Takahiko Nakazi
  • Tomoko Osawa

Abstract

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.

Suggested Citation

  • Takahiko Nakazi & Tomoko Osawa, 2001. "Finite-rank intermediate Hankel operators on the Bergman space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:909041
    DOI: 10.1155/S0161171201001971
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