Geodesic
Radial growth of functions in the Korenblum space
Algebra i analiz, Tome 21 (2009) no. 6, pp. 47-65 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The radial behavior of analytic and harmonic functions that admit a certain majorant in the unit disk is studied. We prove that the extremal growth or decay may occur only along small sets of radii and give precise estimates for these exceptional sets.
Keywords: spaces of analytic functions in the disk, harmonic functions, boundary values, Korenblum spaces. 
@article{AA_2009_21_6_a1,
     author = {A. Borichev and Yu. Lyubarskiǐ and E. Malinnikova and P. Thomas},
     title = {Radial growth of functions in the {Korenblum} space},
     journal = {Algebra i analiz},
     pages = {47--65},
     year = {2009},
     volume = {21},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2009_21_6_a1/}
}
TY  - JOUR
AU  - A. Borichev
AU  - Yu. Lyubarskiǐ
AU  - E. Malinnikova
AU  - P. Thomas
TI  - Radial growth of functions in the Korenblum space
JO  - Algebra i analiz
PY  - 2009
SP  - 47
EP  - 65
VL  - 21
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/AA_2009_21_6_a1/
LA  - en
ID  - AA_2009_21_6_a1
ER  - 
%0 Journal Article
%A A. Borichev
%A Yu. Lyubarskiǐ
%A E. Malinnikova
%A P. Thomas
%T Radial growth of functions in the Korenblum space
%J Algebra i analiz
%D 2009
%P 47-65
%V 21
%N 6
%U http://geodesic.mathdoc.fr/item/AA_2009_21_6_a1/
%G en
%F AA_2009_21_6_a1
A. Borichev; Yu. Lyubarskiǐ; E. Malinnikova; P. Thomas. Radial growth of functions in the Korenblum space. Algebra i analiz, Tome 21 (2009) no. 6, pp. 47-65. http://geodesic.mathdoc.fr/item/AA_2009_21_6_a1/

[1] Bagemihl F., Seidel W., “Some boundary properties of analytic functions”, Math. Z., 61 (1954), 186–199 | DOI | MR | Zbl

[2] Borichev A., “On the minimum of harmonic functions”, J. Anal. Math., 89 (2003), 199–212 | DOI | MR | Zbl

[3] Borichev A., Lyubarskii Yu., “Uniqueness theorems for Korenblum type spaces”, J. Anal. Math., 103 (2007), 307–329 | DOI | MR | Zbl

[4] Cabrelli C., Mendivil F., Molter U., Shonkwiler R., “On the Hausdorff $h$-measure of Cantor sets”, Pacific J. Math., 217:1 (2004), 45–59 | DOI | MR | Zbl

[5] Eiderman V. Ya., “O sravnenii mery Khausdorfa i emkosti”, Algebra i analiz, 3:6 (1991), 173–188 | MR | Zbl

[6] Garnett J., Marshall D., Harmonic measure, New Math. Monogr., 2, Cambridge Univ. Press, Cambridge, 2005, 571 pp. | MR | Zbl

[7] Heinonen J., Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001 | MR

[8] Horowitz C., “Zeros of functions in the Bergman spaces”, Duke Math. J., 41 (1974), 693–710 | DOI | MR | Zbl

[9] Kahane J.-P., Katznelson Y., “Sur le comportement radial des fonctions analytiques”, C. R. Acad. Sci. Paris Sér. A–B, 272 (1971), A718–A719 | MR

[10] Korenblum B., “An extension of the Nevanlinna theory”, Acta Math., 135:3–4 (1975), 187–219 | DOI | MR | Zbl

[11] Nikolskii N. K., Izbrannye zadachi vesovoi approksimatsii i spektralnogo analiza, Tr. Mat. in-ta AN SSSR, 120, 1974, 272 pp. | MR

[12] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.–L., 1950

[13] Seip K., “On Korenblum's density condition for the zero sequences of $A^{-\infty}$”, J. Anal. Math., 67 (1995), 307–322 | DOI | MR | Zbl