Biduals of weighted banach spaces of analytic functions

Abstract

For a positive continuous weight function v on an open subset G of C , let Hv(G) and HVQ(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions / on G such that vf is bounded and vf vanishes at infinity, respectively.

Classical operators on weighted Banach spaces of entire functions

“…Hence, from the τ co -compactness of the closed unit ball and the τ co -continuity of T, [4] and [6]. It is a well-known fact that…”

Schur spaces and weighted spaces of typeH∞

“…This is also true if we deal with G = C and we consider any radial weight which is rapidly decreasing at infinity (i.e., H v (C) contains the polynomials). These results can be found in [5] and some extensions dealing with domains G ⊂ C n , n > 1, can be found in [2]. Boyd and Rueda have studied this problem recently connecting it with the study of M-ideals in weighted spaces of holomorphic functions (see [13]).…”

“…These spaces are Banach spaces endowed with the norm · v and they appear in the study of growth conditions of analytic functions. We refer to [1], [3], [4], [5], [16], [17], [23], [25], and others for further information about these spaces. The study of composition operators on these spaces can be found in [7], [8] and [10].…”

On the isomorphism classes of weighted spaces of harmonic and holomorphic functions

“…Therefore we also have Hv ∼ l ∞ . (Alternatively, we could have used Proposition 5.2 or [1,18] to see that hv ∼ (hv) * * 0 ∼ l ∞ and Hv ∼ (Hv) * * 0 ∼ l ∞ . )…”