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On the Relation Between Fourier and Leont′ev Coefficients with Respect to Smirnov Spaces

B. Forster

Ukrainian Mathematical Journal, vol. 56, no. 4, pp. 628-640, April 2004.



Yu. Mel′nik showed that the Leont′ev coefficients κƒ(λ) in the Dirichlet series ƒ ∼ ∑λ∈Λ κƒ(λ) (eλ⋅)⁄L′(λ) of a function ƒ ∈ Ep(D), 1 < p < ∞, are the Fourier coefficients of some function FLp([0, 2π]) and that the first modulus of continuity of F can be estimated by first moduli and majorants in ƒ. In the present paper, we extend his results to moduli of arbitrary order.


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AUTHOR="Forster, B.",
TITLE="On the Relation Between {F}ourier and {L}eont'ev Coefficients
        with Respect to {S}mirnov Spaces",
JOURNAL="Ukrainian Mathematical Journal",
YEAR="2004",
volume="56",
number="4",
pages="628--640",
month="April",
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