On Mohanty's Criterion for Absolute Convergence of Fourier Series.
Prem Chandra (1973)
Monatshefte für Mathematik
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Prem Chandra (1973)
Monatshefte für Mathematik
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Jouni Luukkainen (1991)
Monatshefte für Mathematik
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James S.W. Wong (1966)
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Heinz W. Engl, Anton Wakolbinger (1985)
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Walter Schempp, Bernd Dreseler (1975)
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M. Nedeljkov, S. Pilipovic, D. Scarpalezos (1996)
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Gavin Brown, St. Koumandos (1997)
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C. Samuel (1996)
Monatshefte für Mathematik
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Ferenc Móricz (2008)
Colloquium Mathematicae
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We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if for all...
C.W. Onneweer (1984)
Monatshefte für Mathematik
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Younis, M.S. (1992)
International Journal of Mathematics and Mathematical Sciences
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Stefano Meda, Rita Pini (1988)
Monatshefte für Mathematik
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Ferenc Móricz (2010)
Studia Mathematica
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We consider complex-valued functions f ∈ L¹(ℝ), and prove sufficient conditions in terms of f to ensure that the Fourier transform f̂ belongs to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes zyg(α) and zyg(α) for some 0 < α ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary in the case of real-valued functions f for which either xf(x) ≥ 0 or f(x) ≥ 0 almost everywhere.
Walter R. Bloom, Zengfu Xu (1998)
Monatshefte für Mathematik
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K. Hag, K. Astala, P. Hag, V. Lappalainen (1993)
Monatshefte für Mathematik
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