Geodesic
Weakly cyclic vectors with a given modulus
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 111-118 
E. Doubtsov. Weakly cyclic vectors with a given modulus. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 111-118. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a5/
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     author = {E. Doubtsov},
     title = {Weakly cyclic vectors with a~given modulus},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a5/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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. We construct weakly cyclic vectors with a prescribed lower semicontinuous modulus of the boundary values.

[1] V. I. Smirnov, “Sur les valeurs limites des fonctions, regulières à l'interieur d'un cercle”, Zh. Leningr. fiz.-mat. ob-va, 2:2 (1929), 22–37

[2] U. Rudin, Teoriya funktsii v polikruge, Mir, M., 1974 | MR | Zbl

[3] A. B. Aleksandrov, “Essays on non locally convex Hardy spaces”, Lect. Notes Math., 864, Springer-Verlag, 1981, 1–89 | MR

[4] A. P. Frazier, “The dual space of $H^p$ of the polydisc for $0

1$”, Duke Math. J., 39 (1972), 369–379 | DOI | MR | Zbl

[5] A. B. Aleksandrov, “Vnutrennie funktsii na kompaktnykh prostranstvakh”, Funkts. anal. i ego pril., 18:2 (1984), 1–13 | MR | Zbl

[6] E. Doubtsov, “Little Bloch functions, symmetric pluriharmonic measures and Zygmund's dichotomy”, J. Funct. Anal., 170 (2000), 286–306 | DOI | MR | Zbl