Geodesic
Double cosine-sine series and Nikol'skii classes in uniform metric
Problemy analiza, Tome 8 (2019) no. 3, pp. 187-203

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In the this paper, we give neccessary and sufficient conditions for a function even with respect to the first argument but odd with respect to the second one to belong to the Nikol'skii classes defined by a mixed modulus of smoothness of a mixed derivative (both have arbitrary integer orders). These conditions involve the growth of partial sum of Fourier cosine-sine coefficients with power weights or the rate of decreasing to zero of these coefficients. A similar problem for generalized "small" Nikol'skii classes is also treated.
Keywords: double cosine-sine series, mixed modulus of smoothness, Nikol'skii classes. 
@article{PA_2019_8_3_a16,
     author = {S. S. Volosivets},
     title = {Double cosine-sine series and {Nikol'skii} classes in uniform metric},
     journal = {Problemy analiza},
     pages = {187--203},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a16/}
}
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S. S. Volosivets. Double cosine-sine series and Nikol'skii classes in uniform metric. Problemy analiza, Tome 8 (2019) no. 3, pp. 187-203. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a16/