On Double Sine and Cosine Transforms, Lipschitz and Zygmund Classes

• DOI: 10.1007/s10496-011-0351-9
• Publication Date: 2012-01-03T06:16:21Z
• Authors: Vanda Fülöp Vanda...; Ferenc Mόricz Fer...
• Keywords: Sine

We consider complex-valued functions f ∈ L1(R+2), where R+:= [0,∞), and prove sufficient conditions under which the double sine Fourier transform \(\hat f_{ss} \) and the double cosine Fourier transform \(\hat f_{cc} \) 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 ∈ L1(R+2).