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

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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. 
@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},
     publisher = {mathdoc},
     volume = {188},
     number = {8},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_8_a9/}
}
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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/