Ukrainian Mathematical Journal

, Volume 56, Issue 4, pp 628–640

On the relation between fourier and leont’ev coefficients with respect to smirnov spaces

  • B. Forster
Article

Abstract

Yu. Mel’nik showed that the Leont’ev coefficients Κf(λ) in the Dirichlet series \({{2n} \mathord{\left/ {\vphantom {{2n} {\left( {n + 1} \right) < p < 2}}} \right. \kern-\nulldelimiterspace} {\left( {n + 1} \right) < p > 2}}\) of a function fEp(D), 1 < p < ∞, are the Fourier coefficients of some function FLp, ([0, 2π]) and that the first modulus of continuity of F can be estimated by the first moduli and majorants in f. In the present paper, we extend his results to moduli of arbitrary order.

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • B. Forster
    • 1
  1. 1.Zentrum MathematikTechnische Universität MünchenGermany

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