Operators on weighted Bergman spaces
نویسنده
چکیده
Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operators L(A1,ρ(D), X) is isomorphic to Blochρ(X) and some applications of this result are presented. Several properties of generalized vector-valued Bloch functions are also considered.
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تاریخ انتشار 2004