On the primary ideal structure at infinity for analytic Beurling algebras

Abstract

An algebra B is a Banach algebra if there is a norm defined on it such that B is a Banach space and the multiplication is continuous. As far as we are concerned, all Banach algebras are assumed commutative. For standard facts in the elementary theory of commutative Banach algebras we refer to [10] and [22]. Suppose w is a locally bounded measurable (weight) function on R, which satisfies ~ w(x) >= 1, x~ll, (0.1) t w ( x + y ) <= w(x)w(y), x, yER. Then the space L~w (R) of (equivalence classes of) functions f, Lebesgue measurable on R and satisfying {Ifll w = f 2= If(x)lw (x) dx < ~o