Geodesic
Approximability of the classes $B_{p,\theta}^r$ of periodic functions
Sbornik. Mathematics, Tome 195 (2004) no. 2, pp. 237-261

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Several questions of the approximability by linear methods of the Besov classes $B_{1,\theta}^r$ and $B_{p,\theta}^r$ of periodic functions of several variables, $1\leqslant p\infty$, are considered alongside their best approximations in the spaces $L_1$ and $L_\infty$, respectively. Taken for approximation aggregates are trigonometric polynomials with spectrum in the step hyperbolic cross. Sharp (in order) estimates of the deviations of step hyperbolic Fourier sums on the classes $B_{p,\theta}^r$, $1\leqslant p\infty$, in the $L_\infty$ space are also obtained. 
@article{SM_2004_195_2_a3,
     author = {A. S. Romanyuk},
     title = {Approximability  of the classes $B_{p,\theta}^r$ of periodic functions},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_2_a3/}
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A. S. Romanyuk. Approximability  of the classes $B_{p,\theta}^r$ of periodic functions. Sbornik. Mathematics, Tome 195 (2004) no. 2, pp. 237-261. http://geodesic.mathdoc.fr/item/SM_2004_195_2_a3/