“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 2328  


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 L^{1}_{a} (G) then H^{∞} (G) is dense in L^{p}_{a} (G) , p > 1.
Download TeX format 

back to top 