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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, Moscow, Steklov Mathematical Institute of RAS

Approximation by polynomials in Bergman spaces

R. Akgun

Balıkesir University

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.

Language: English

References
  1. 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  mathscinet
  2. E. A. Storozhenko, “On a Hardy–Littlewood problem”, Mat. Sb. (N.S.), 119 (161):4 (1982), 564–583  mathnet  mathscinet
  3. 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  mathscinet  zmath

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