The Fourier transforms of Lipschitz functions on certain domains.
Younis, M.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (2001)
International Journal of Mathematics and Mathematical Sciences
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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.
Younis, M.S. (1992)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (2000)
International Journal of Mathematics and Mathematical Sciences
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Raimond Struble (1984)
Studia Mathematica
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R. Bhuvaneswari, V. Karunakaran (2010)
Annales UMCS, Mathematica
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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
R. Bhuvaneswari, V. Karunakaran (2010)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
Tong-Seng Quek, Leonard Y.H. Yap (1983)
Mathematische Zeitschrift
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Louis Pigno (1981)
Colloquium Mathematicae
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S. Hartman (1975)
Colloquium Mathematicae
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Colin C. Graham (1976)
Colloquium Mathematicae
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Schmeelk, John (1990)
International Journal of Mathematics and Mathematical Sciences
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Nicolas Artémiadis (1967)
Compositio Mathematica
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