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


We consider Hölder-Zygmund spaces of -periodic functions , where the -th difference with step-size of the -th derivative in the - or -norm is bounded by a modulus-type function . For the Fourier sum and related approximation processes we investigate error estimates in corresponding Hölder-Zygmund norms if the smoothness of 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