Riesz projection, Smirnov class, Herglotz integral, singular measure, Beurling's theorem, backward shift, pseudocontinuation
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 ∩ H^p [overscore over the second H^p]. This leads to a natural analog of the Riesz projection on a certain quotient space of L^p for p ϵ (0, 1). We also study a Herglotz-like integral transform for singular measures on the unit circle ∂D.
© 2005 American Mathematical Society
Garcia, S.R., A *-closed subalgebra of the Smirnov class, Proc. Amer. Math. Soc. 133, no. 7, (2005), 2051–2059. MR2137871 (2005m:30040)