On double sine and cosine transforms,Lipschitz and Zygmund classes |
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Authors: | Vanda Fülöp Ferenc Móricaz |
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Affiliation: | 1.University of Szeged,Szeged,Hungary;2.Bolyai Institute,University of Szeged,Szeged,Hungary |
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Abstract: | We consider complex-valued functions f ∈ L 1(R +2), where R +:= [0,∞), and prove sufficient conditions under which the double sine Fourier transform [^(f)]sshat f_{ss} and the double cosine Fourier transform [^(f)]cchat f_{cc} belong to one of the two-dimensional Lipschitz classes Lip(α, β) for some 0 < α, β ≤ 1; or to one of the Zygmund classes Zyg(α, β) for some 0 < α, β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1(R +2). |
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