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 $f \in L^1(\mathbf{R}^2_+)$, where $\mathbf{R}_+ := [0,\infty)$, 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 $Lip(\alpha,\beta )$ for some $0 < \alpha,\beta \leq 1$; or to one of the Zygmund classes Zyg$(\alpha,\beta )$ for some $0 < \alpha,\beta \leq 2$. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions $f \in L^1(\mathbf{R}^2_+)$.
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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
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