JournalszaaVol. 9, No. 4pp. 343–349

Error Estimates in Generalized Trigonometric Hölder-Zygmund Norms

  • Jürgen Prestin

    Universität zu Lübeck, Germany
  • Siegfried Prössdorf

    Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
Error Estimates in Generalized Trigonometric Hölder-Zygmund Norms cover
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Abstract

We consider Hölder-Zygmund spaces of 2π2\pi-periodic functions f:RCf: \mathbb R \to \mathbb C, where the kk-th difference with step-size hh of the rr-th derivative in the LpL^p- or CC-norm is bounded by a modulus-type function ω(h)\omega (h). For the Fourier sum and related approximation processes we investigate error estimates in corresponding Hölder-Zygmund norms if the smoothness of ff is given by other Hölder-Zygmund conditions. The convergence order for the general case can be formulated in a simple manner. This allows us to state also Jackson-type theorems for such Banach spaces. Moreover, we give explicit values for the constants appearing in these estimates.

Cite this article

Jürgen Prestin, Siegfried Prössdorf, Error Estimates in Generalized Trigonometric Hölder-Zygmund Norms. Z. Anal. Anwend. 9 (1990), no. 4, pp. 343–349

DOI 10.4171/ZAA/406