Dowling, Thomas and O'Farrell, Anthony G. (1995) Affine transformations and analytic capacities. Transactions of the American Mathematical Society, 347. pp. 26432655. ISSN 00029947
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Abstract
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 Beurlingâ€“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; CalderonZygmund; Nonbanach 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 
URI: 
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