Ukrainian Mathematical Journal

, Volume 56, Issue 4, pp 628–640 | Cite as

On the relation between Fourier and Leont’ev coefficients with respect to smirnov spaces

  • B. Forster


Yu. Mel’nik showed that the Leont’ev coefficients Κ f (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 fE p (D), 1 < p < ∞, are the Fourier coefficients of some function FL p , ([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.


Fourier Coefficient Arbitrary Order Dirichlet Series Smirnov Space 
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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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