C1 Changes of Variable: Beurling-Helson Type Theorem and Hörmander Conjecture on Fourier Multipliers.
V. Lebedev, A. Olevskii (1994)
Geometric and functional analysis
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V. Lebedev, A. Olevskii (1994)
Geometric and functional analysis
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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.
Younis, M.S. (2000)
International Journal of Mathematics and Mathematical Sciences
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O.Carruth McGehee (1979)
Mathematische Annalen
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Thomas M. MacRobert (1961)
Mathematische Zeitschrift
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Louis Pigno, Sadahiro Saeki (1975)
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M. Wojciechowski (2002)
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