2017
Том 69
№ 6

All Issues

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

Forster B.

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Abstract

Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series \({{2n} \mathord{\left/ {\vphantom {{2n} {\left( {n + 1} \right) < p < 2}}} \right. \kern-0em} {\left( {n + 1} \right) < p > 2}}\) 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.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 4, pp 628-640.

Citation Example: Forster B. On the relation between fourier and leont’ev coefficients with respect to smirnov spaces // Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 517–526.

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