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Zapiski Nauchnykh Seminarov LOMI, 1985, Volume 141, Pages 5–17
(Mi znsl4085)
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This article is cited in 2 scientific papers (total in 2 papers)
Hankel operators and problems of best approximation of unbounded functions
A. L. Vol'berg, V. A. Tolokonnikov
Abstract:
For each function $f$, $f\in VMO$, there exist a unique function $f_0$, analytic in the circle $\mathbb D$ and such that $\|f-f_0\|_\infty=\inf\{\|f-g\|_\infty\colon g\in VMO_A\}$. We define the operator of best approximation (nonlinear) $\mathcal A$, $\mathcal Af=f_0$, $f\in VMO$. In the paper one considers the question of the preservation of a class under the action of the operator i.e. finding the classes $X$, $X\subset VMO$, $\mathcal AX\subset X$. One investigates the classes $X$ containing unbounded functions. It is proved that if $P_-X$ is the space of the symbols of the Hankel operators from a Banach space $E$ of functions into the Hardy space $H^2$, then $\mathcal AX\subset X$. For $E$ one can take “almost” any space.
Citation:
A. L. Vol'berg, V. A. Tolokonnikov, “Hankel operators and problems of best approximation of unbounded functions”, Investigations on linear operators and function theory. Part XIV, Zap. Nauchn. Sem. LOMI, 141, "Nauka", Leningrad. Otdel., Leningrad, 1985, 5–17; J. Soviet Math., 37:5 (1987), 1269–1275
Linking options:
https://www.mathnet.ru/eng/znsl4085 https://www.mathnet.ru/eng/znsl/v141/p5
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Abstract page: | 181 | Full-text PDF : | 88 |
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