@Article{ATA-27-4,
author = {Vanda, Fülöp,  and Mόricz, Ferenc},
title = {On Double Sine and Cosine Transforms, Lipschitz and Zygmund Classes},
journal = {Analysis in Theory and Applications},
year = {2011},
volume = {27},
number = {4},
pages = {351--364},
abstract = {<p style="text-align: justify;">We consider complex-valued functions $f \in &nbsp;L^1(\mathbf{R}^2_+)$, 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 $\hat{f}_{cc}$ &nbsp;belong to one of the two-dimensional Lipschitz classes $Lip(\alpha,\beta )$ for some $0 &lt; \alpha,\beta \leq 1$; or to one of the Zygmund classes Zyg$(\alpha,\beta )$ for some $0 &lt; \alpha,\beta &nbsp;\leq 2$. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions $f \in L^1(\mathbf{R}^2_+)$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.1007/s10496-011-0351-9},
url = {https://global-sci.com/article/74120/on-double-sine-and-cosine-transforms-lipschitz-and-zygmund-classes}
}