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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 303, Pages 111–118 (Mi znsl903)  

Weakly cyclic vectors with a given modulus

E. Doubtsov

Saint-Petersburg State University
References:
Abstract: Let $H^p$ be the Hardy space in the polydisc. Denote by $\mathcal P$ the set of all holomorphic polynomials. A vector $f\in H^p$ is called weakly cyclic if the product $f\mathcal P$ is weakly dense in $H^p$, $0<p<1$. We construct weakly cyclic vectors with a prescribed lower semicontinuous modulus of the boundary values.
Received: 10.07.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 129, Issue 4, Pages 3990–3993
DOI: https://doi.org/10.1007/s10958-005-0335-4
Bibliographic databases:
UDC: 517.55
Language: Russian
Citation: E. Doubtsov, “Weakly cyclic vectors with a given modulus”, Investigations on linear operators and function theory. Part 31, Zap. Nauchn. Sem. POMI, 303, POMI, St. Petersburg, 2003, 111–118; J. Math. Sci. (N. Y.), 129:4 (2005), 3990–3993
Citation in format AMSBIB
\Bibitem{Dou03}
\by E.~Doubtsov
\paper Weakly cyclic vectors with a~given modulus
\inbook Investigations on linear operators and function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 303
\pages 111--118
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl903}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2037534}
\zmath{https://zbmath.org/?q=an:1145.32303}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 4
\pages 3990--3993
\crossref{https://doi.org/10.1007/s10958-005-0335-4}
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