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

 

Maximality theorems for Fréchet algebras


Authors: Zeljko Cuckovic and N. V. Rao
Journal: Proc. Amer. Math. Soc. 134 (2006), 487-490
MSC (2000): Primary 30H05, 30D55; Secondary 30E10, 46E25
Published electronically: July 8, 2005
MathSciNet review: 2176017
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Abstract: The algebra of unbounded holomorphic functions $\bigcap_{p \geq 1}H^p(\partial \mathbb{D} )$ that is contained in the algebra $\bigcap_{p \geq 1}L^p(\partial \mathbb{D} )$ is studied. For $f$ in $\bigcap_{p \geq 1}L^p(\partial \mathbb{D} )$ but not in $\bigcap_{p \geq 1}H^p(\partial \mathbb{D} )$, we show that the algebra generated by $\bigcap_{p \geq 1}H^p(\partial \mathbb{D} )$ and $f$ is dense in $L^p(\partial \mathbb{D} )$ for all $p \geq 1$.


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Additional Information

Zeljko Cuckovic
Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
Email: zcuckovi@math.utoledo.edu

N. V. Rao
Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
Email: rnagise@math.utoledo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08008-1
PII: S 0002-9939(05)08008-1
Received by editor(s): September 16, 2003
Received by editor(s) in revised form: September 23, 2004
Published electronically: July 8, 2005
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2005 American Mathematical Society