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 F ∈ Lp([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",
note="")
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