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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Corrected outer functions


Author: Evgueni Doubtsov
Journal: Proc. Amer. Math. Soc. 126 (1998), 515-522
MSC (1991): Primary 30D50; Secondary 30D55
MathSciNet review: 1415583
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Abstract: Given $0<p<2$ and a strictly positive continuous function $\varphi $ on the unit circle, we construct a bounded analytic function $g$ such that $|g^{*}|=\varphi $ a.e., and $g$ is in the Besov space $A_{p}^{1}$ on the unit disc.


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Additional Information

Evgueni Doubtsov
Affiliation: Centre de Recerca Matemàtica, Institut d’Estudis Catalans, Apartat 50, E-08193 Bellaterra, Barcelona, Spain
Address at time of publication: ul. Partizana Germana 14/117, kv. 335, 198205 St. Petersburg, Russia
Email: doubtsov@crm.es, es@dub.pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04054-4
PII: S 0002-9939(98)04054-4
Keywords: Hardy classes, Besov space, inner-outer factorization
Received by editor(s): March 13, 1996
Received by editor(s) in revised form: August 13, 1996
Additional Notes: Supported by the Centre de Recerca Matemàtica, Institut d’Estudis Catalans (Barcelona) under a grant from DGICYT (Spain).
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society