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International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 27, 2015 14:30–14:55, Приближения функций и гармонический анализ, Moscow, Steklov Mathematical Institute of RAS
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Approximation by polynomials in Bergman spaces
R. Akgun
Balıkesir University
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Abstract:
The purpose of this work is to obtain Jackson and converse inequalities of
polynomial approximation in Bergman spaces. Some known results, proved for
moduli of continuity, are extended to the moduli of smoothness. We proved
some simultaneous approximation theorems and obtained the Nikolskii-Stechkin
inequality for polynomials in these spaces.
Supplementary materials:
abstract.pdf (73.5 Kb)
Language: English
References
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M. Sh. Shabozov, O. Sh. Shabozov, “Best approximation and the value of the widths of some classes of functions in the Bergman space $B_{p}$, $1\leq p\leq \infty$”, Dokl. Akad. Nauk, 410:4 (2006), 661–664
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E. A. Storozhenko, “On a Hardy–Littlewood problem”, Mat. Sb. (N.S.), 119 (161):4 (1982), 564–583
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Xing Fu Chong, “A Bernstein-type inequality in Bergman spaces $B_{q}^{p}$, $p>0$, $q>1$”, Acta Math. Sinica (Chin. Ser.), 49:2 (2006), 431–434
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