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A -closed subalgebra of the Smirnov class

Author(s): Stephan Ramon Garcia
Journal: Proc. Amer. Math. Soc. 133 (2005), 2051-2059.
MSC (2000): Primary 30D55
Posted: January 14, 2005
MathSciNet review: 2137871
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Abstract: We study real Smirnov functions and investigate a certain -closed subalgebra of the Smirnov class containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space $H^p \cap \overline{H^p}$ . This leads to a natural analog of the Riesz projection on a certain quotient space of for $p \in (0,1)$ . We also study a Herglotz-like integral transform for singular measures on the unit circle $\partial \mathbb{D}$ .

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Additional Information:

Stephan Ramon Garcia
Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080
Email: garcias@math.ucsb.edu

DOI: 10.1090/S0002-9939-05-07735-X
PII: S 0002-9939(05)07735-X
Keywords: Riesz projection, Smirnov class, Herglotz integral, singular measure, Beurling's theorem, backward shift, pseudocontinuation
Received by editor(s): February 3, 2004
Received by editor(s) in revised form: March 5, 2004
Posted: January 14, 2005
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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