On the relation between Fourier and Leont’ev coefficients with respect to Smirnov spaces - Forster, B. (Український математичний журнал, 2004)
Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series 2n/(n+1) 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.