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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

Abstract:

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) : B → C of evaluation at λ ∈ G given by e (λ) (f) = f(λ) is bounded, and if f ∈ B then zf ∈ B . 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 L¹_a (G) then H^∞ (G) is dense in L^p_a (G) , p > 1.

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