Geodesic
Widths of the unit ball in $H^\infty$ in weighted spaces $L_q(\mu)$
Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1259-1267 
O. G. Parfenov. Widths of the unit ball in $H^\infty$ in weighted spaces $L_q(\mu)$. Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1259-1267. http://geodesic.mathdoc.fr/item/SM_1997_188_8_a9/
@article{SM_1997_188_8_a9,
     author = {O. G. Parfenov},
     title = {Widths of the unit ball in $H^\infty$ in weighted spaces~$L_q(\mu)$},
     journal = {Sbornik. Mathematics},
     pages = {1259--1267},
     year = {1997},
     volume = {188},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_8_a9/}
}
TY  - JOUR
AU  - O. G. Parfenov
TI  - Widths of the unit ball in $H^\infty$ in weighted spaces $L_q(\mu)$
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 1259
EP  - 1267
VL  - 188
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_8_a9/
LA  - en
ID  - SM_1997_188_8_a9
ER  - 
%0 Journal Article
%A O. G. Parfenov
%T Widths of the unit ball in $H^\infty$ in weighted spaces $L_q(\mu)$
%J Sbornik. Mathematics
%D 1997
%P 1259-1267
%V 188
%N 8
%U http://geodesic.mathdoc.fr/item/SM_1997_188_8_a9/
%G en
%F SM_1997_188_8_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

The study of the widths of the unit ball in the Hardy space $H^\infty$ in weighted spaces $L_q(\mu)$ is carried out. Sharp lower estimates of these widths in terms of the capacity of the support of the measure $\mu$ are obtained. The precise values of the widths are calculated for Blaschke lemniscates. For the measures $d\mu =p\,dS$, where $dS$ is plane Lebesgue measure and $p$ is a positive continuous weight, an asymptotic formula is found.

[1] Parfenov O. G., “Poperechniki edinichnogo shara $H^\infty$ v vesovykh prostranstvakh $L_q(\mu)$”, Funkts. analiz i ego prilozh., 26:3 (1992), 85–87 | MR | Zbl

[2] Fisher S., Micchelli C., “The $n$-widths of sets of analytic functions”, Duke Math. J., 47:4 (1980), 789–801 | DOI | MR | Zbl

[3] Fisher S., Stessin M. I., The $n$-widths of unit ball of $H^q$, Northwestern University, Evanston, 1990 | MR

[4] Osipenko K. Yu., Stesin M. I., “O poperechnikakh klassa $H^2$ v $n$-mernom share”, UMN, 45:5 (1990), 193–194 | MR | Zbl

[5] Parfenov O. G., “Poperechniki po Gelfandu nekotorykh klassov analiticheskikh funktsii”, Matem. sb., 185:6 (1994), 105–112 | MR | Zbl

[6] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[7] Parfenov O. G., “Poperechniki po Gelfandu edinichnogo shara klassa Khardi $H^p$ v vesovykh prostranstvakh”, Matem. zametki, 37:2 (1985), 171–175 | MR | Zbl

[8] Pich A., Operatornye idealy, Mir, M., 1982 | MR

[9] Parfenov O. G., “Otsenki singulyarnykh chisel operatora vlozheniya Karlesona”, Matem. sb., 131:4 (1986), 501–518 | MR