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Bounded Functions in Möbius Invariant Dirichlet Spaces

✍ Scribed by Artur Nicolau; Jie Xiao

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
557 KB
Volume
150
Category
Article
ISSN
0022-1236

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✦ Synopsis

For p # (0, 1), let Q p (Q p, 0 ) be the space of analytic functions f on the unit disk

, where &} & D p means the weighted Dirichlet norm and . w is the Mo bius map of 2 onto itself with . w (0)=w. In this paper, we prove the Corona theorem for the algebra

then we provide a Fefferman Stein type decomposition for Q p (Q p, 0 ), and finally we describe the interpolating sequences for

1997 Academic Press where dm(z) denotes the usual Lebesgue measure on 2. These are called Dirichlet type spaces because for p=0 one gets the classical Dirichlet space D of all analytic functions on 2 whose images have finite area, counting multiplicities. Also, observe that for p=1, D p is just the usual Hardy space H 2 and for p>1 is the Bergman space with weight (1& |z| 2 ) p&2 .

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