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Growth estimates for generalized factors of $H^p$ spaces

Tom 158 / 2003

Studia Mathematica 158 (2003), 19-38 MSC: 30D55, 47B35. DOI: 10.4064/sm158-1-3

Streszczenie

With $\varphi$ an inner function and $M_{\varphi }$ the multiplication operator on a given Hardy space it is known that for any given function $f$ in the Hardy space we may use the Wold decomposition to obtain a factorization of the given $f$ (not the Riesz factorization). This new factorization has been shown to be useful in the study of commutants of Toeplitz operators.

We study the smoothness of each factor of this factorization. We show in some cases that the factors lie in the same Hardy space (or smoothness class) as the given function $f$. We also construct an example to show that there are bounded, holomorphic functions which have factors that are not in a given Hardy $p$-space. Many of our results are produced by studying a natural class of positive measures associated to the given inner function.

Autorzy

• Joseph A. CimaDepartment of Mathematics
University of North Carolina
346 Phillips Hall 3250
Chapel Hill, NC 27599-3250, U.S.A.
e-mail
• Angeliki KazasDepartment of Mathematics,
Computer Science, and Statistics
SUNY at Oneonta
Oneonta, NY 13820, U.S.A.
e-mail
• Michael I. StessinDepartment of Mathematics and Statistics
SUNY at Albany
Albany, NY 12222, U.S.A.
e-mail

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