On Double Sine and Cosine Transforms, Lipschitz and Zygmund Classes
Year: 2011
Author: Vanda Fülöp, Ferenc Mόricz
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 4 : pp. 351–364
Abstract
We consider complex-valued functions f∈L1(R2+), where R+:=[0,∞), and prove sufficient conditions under which the double sine Fourier transform ˆfss and the double cosine Fourier transform ˆfcc 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(R2+).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.1007/s10496-011-0351-9
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 4 : pp. 351–364
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: double sine and cosine Fourier transform Lipschitz class Lip$(\alpha \beta)$ $0< \alpha \beta \leq 1$ Zygmund class Zyg$(\alpha $0 < \alpha \beta \leq 2$.
Author Details
Vanda Fülöp Email
Ferenc Mόricz Email
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