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A Factoring Theorem for The Bergman Space
Author(s) -
Hedenmalm Håkan
Publication year - 1994
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/26.2.113
Subject(s) - factoring , mathematics , citation , space (punctuation) , arithmetic , algebra over a field , library science , computer science , pure mathematics , finance , economics , operating system
0. Introduction Let D be the open unit disk in the complex plane C, T the unit circle, and L(D) the Bergman space, consisting of those analytic functions on D that are square integrable on D with respect to area measure. The Bergman space is a closed subspace of the Hilbert space L(O) of all square area-integrable complex-valued functions on D. The inner product in L(D), and hence in L(D), is given by the formula f L*= J{z)g(z)dA(z), /geL(D), Jo where dA denotes planar area measure, normalized so that D has total mass 1. The associated norm is denoted by || • ||L2. The Hardy space 77 (B) consists of all functions /holomorphic on O satisfying