Maximality theorems for Fréchet algebras
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- by Željko Čučković and N. V. Rao PDF
- Proc. Amer. Math. Soc. 134 (2006), 487-490 Request permission
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 $p \geq 1$.References
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Additional Information
- Željko Čučković
- Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
- MR Author ID: 294593
- Email: zcuckovi@math.utoledo.edu
- N. V. Rao
- Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
- Email: rnagise@math.utoledo.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 487-490
- MSC (2000): Primary 30H05, 30D55; Secondary 30E10, 46E25
- DOI: https://doi.org/10.1090/S0002-9939-05-08008-1
- MathSciNet review: 2176017