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Weighted Spaces of Holomorphic Functions on Finitely Connected Domains

✍ Scribed by Päivi Mattila

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
644 KB
Volume
189
Category
Article
ISSN
0025-584X

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✦ Synopsis

Q. The conditions on the weights are expressed in terms of the hyperbolic metric in Corollary 3.2 and in terms of the Euclidean metric in Corollary 4.1.

We denote IN = { 1,2,. . . } and IN0 = {0,1, . . . } . Let D denote the open unit disk of Q: and Q: oo the extended complex plane. q, denotes the Banach space consisting of the sequences which converge to 0, equipped with the sup-norm. We denote isomorphic Banach spaces X and Y by X -Y .

Let v be a (strictly) positive continuous weight function on a domain G of C (or on a Jordan domain G of Cm). Put

Hv(G)

Hv (G) and Hvo(G), both endowed with the norm Ilfllv, are Banach spaces.

If J c Q: is a Jordan curve, the bounded component of C \ J is the inner domain of J ; the union of (00) and the unbounded component of C \ J is the outer domain of J . For A C C , dist(A, J ) denotes the distance between the sets A and J , defined by the Euclidean distance (see [He], p. 109).

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