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| Paper IPM / M / 2328 |
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| Abstract: | |
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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 L1a (G) then H∞ (G) is dense in Lpa (G) , p > 1.
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