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Paper   IPM / M / 2328
School of Mathematics
  Title:   Multipliers in certain Banach spaces of analytic functions
  Author(s):  K. Hedayatian
  Status:   Published
  Journal: Korean Ann. Math.
  Vol.:  21
  Year:  2004
  Pages:   65-72
  Supported by:  IPM
Let G be a bounded domain in the complex plane C. A Banach space of analytic functions on G is a Banach space B consisting of functions that are analytic on G such that 1 ∈ B , the functional e(λ) : BC of evaluation at λ ∈ G given by e (λ) (f) = f(λ) is bounded, and if fB then zfB . The collection of all multipliers of B is denoted by M (B ). In this article, we give sufficient conditions so that M (B ) = H(G ) ∩B = H . Also we show that if the number of connected components of ∂G is finite and H (G) is dense in L1a (G) then H (G) is dense in Lpa (G) , p > 1.

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