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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Blaschke products and nonideal ideals in higher order Lipschitz algebras


Author: K. M. Dyakonov
Original publication: Algebra i Analiz, tom 21 (2009), nomer 6.
Journal: St. Petersburg Math. J. 21 (2010), 979-993
MSC (2010): Primary 30J10, 30H10, 46J15, 46J20
Published electronically: September 22, 2010
MathSciNet review: 2604546
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Abstract: We investigate certain ideals (associated with Blaschke products) of the analytic Lipschitz algebra $ A^\alpha$, with $ \alpha>1$, that fail to be ``ideal spaces''. The latter means that the ideals in question are not describable by any size condition on the function's modulus. In the case where $ \alpha=n$ is an integer, we study this phenomenon for the algebra $ H^\infty_n=\{f : f^{(n)}\in H^\infty\}$ rather than for its more manageable Zygmund-type version. This part is based on a new theorem concerning the canonical factorization in $ H^\infty_n$.


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Additional Information

K. M. Dyakonov
Affiliation: ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, E-08007 Barcelona, Spain
Email: dyakonov@mat.ub.es

DOI: http://dx.doi.org/10.1090/S1061-0022-2010-01127-0
PII: S 1061-0022(2010)01127-0
Keywords: Inner functions, Blaschke products, Lipschitz spaces, ideals
Received by editor(s): January 14, 2009
Published electronically: September 22, 2010
Additional Notes: Supported in part by grant MTM2008-05561-C02-01 from El Ministerio de Ciencia e Innovación (Spain) and grant 2009-SGR-1303 from AGAUR (Generalitat de Catalunya).
Dedicated: To Victor Petrovich Havin, with admiration (best phrased as a palindrome): \Russian{VOT PEDAGOG ADEPTOV}!
Article copyright: © Copyright 2010 American Mathematical Society