On the relation between fourier and leont’ev coefficients with respect to smirnov spaces - Forster, B. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series \(2n / 2n ( n + 1 ) < p < 2 . -0em ( n + 1 ) < p > 2 \) 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.