Abstract:
Let Rn(f,Hp) be the best approximation to the function f in the Hardy space Hp by rational functions of degree at most n−1. It is shown that, for example, f∈Hp (1<p<∞) satisfies the condition ∑∞k=0(2kαR2k(f,Hp))σ<∞ (α>0, σ=(α+p−1)−1) if and only if f belongs to the Hardy–Besov space Bασ. Rational approximation is also considered in Hp (p⩽1) and H∞. Some applications of the results are given.
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\Bibitem{Pek85}
\by A.~A.~Pekarskii
\paper Classes of analytic functions determined by best rational approximations in~$H_p$
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 1
\pages 1--18
\mathnet{http://mi.mathnet.ru/eng/sm1954}
\crossref{https://doi.org/10.1070/SM1986v055n01ABEH002988}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=791314}
\zmath{https://zbmath.org/?q=an:0593.30040|0578.30032}
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https://doi.org/10.1070/SM1986v055n01ABEH002988
https://www.mathnet.ru/eng/sm/v169/i1/p3
This publication is cited in the following 23 articles:
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