Abstract
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 f ∈E p (D), 1 < p < ∞, are the Fourier coefficients of some function F ∈L 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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 517–526, April, 2004.
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Forster, B. On the relation between Fourier and Leont’ev coefficients with respect to smirnov spaces. Ukr Math J 56, 628–640 (2004). https://doi.org/10.1007/s11253-005-0091-0
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DOI: https://doi.org/10.1007/s11253-005-0091-0