Affine transformations and analytic capacities

Dowling, Thomas and O'Farrell, Anthony G. (1995) Affine transformations and analytic capacities. Transactions of the American Mathematical Society, 347. pp. 2643-2655. ISSN 0002-9947

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Analytic capacities are set functions defined on the plane which may be used in the study of removable singularities, boundary smoothness and approximation of analytic functions belonging to some function space. The symmetric concrete Banach spaces form a class of function spaces that include most spaces usually studied. The Beurling transform is a certain singular integral operator that has proved useful in analytic function theory. It is shown that the analytic capacity associated to each Beurling–invariant symmetric concrete Banach space behaves reasonably under affine transformation of the plane. It is not known how general analytic capacities behave under affine maps.

Item Type: Article
Additional Information: First published in Transactions of the American Mathematical Society in Vol. 347, 1995, published by the American Mathematical Society.
Keywords: Affine transformations; Analytic capacities; Calderon-Zygmund; Non-banach spaces.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1815
Depositing User: Prof. Anthony O'Farrell
Date Deposited: 26 Jan 2010 13:07
Journal or Publication Title: Transactions of the American Mathematical Society
Publisher: American Mathematical Society
Refereed: Yes

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