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On a generalized corona problem on the unit disc

Author(s): Jordi Pau
Journal: Proc. Amer. Math. Soc. 133 (2005), 167-174.
MSC (2000): Primary 30D55; Secondary 46J15
Posted: June 2, 2004
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Abstract: Let $g,f_ 1,\dots,f_ n\in H^{\infty}$. We give a sufficient condition on the size of a function $g$ in order for it to be in the ideal generated by $f_ 1,\dots,f_ n$. In particular, this improves Cegrell's result on this problem.

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Additional Information:

Jordi Pau
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
Email: jpau@mat.uab.es

DOI: 10.1090/S0002-9939-04-07516-1
PII: S 0002-9939(04)07516-1
Keywords: ${H}^p$-spaces, corona problems, Carleson measure
Received by editor(s): January 31, 2003
Received by editor(s) in revised form: September 10, 2003
Posted: June 2, 2004
Additional Notes: The author is supported by the EU Research Training Network HPRN-CT-$2000$-$00116$, and partially supported by SGR grant $2001$SGR$00431$ and DGICYT grant PB$98$-$0872$
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2004, American Mathematical Society

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