A *-closed subalgebra of the Smirnov class

Garcia, Stephan

doi:10.1090/S0002-9939-05-07735-X

A $*$-closed subalgebra of the Smirnov class
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Proc. Amer. Math. Soc. 133 (2005), 2051-2059 Request permission

Abstract:

We study real Smirnov functions and investigate a certain $*$-closed subalgebra of the Smirnov class $N^+$ 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 $L^p$ 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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