2019
Том 71
№ 11

# Forster B.

Articles: 1
Article (English)

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

Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 517–526

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.