Geodesic
Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1364-1368

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Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials in some classes of functions and for the Kolmogorov $N$-widths of these classes. These results find applications in numerical analysis. 
@article{ZVMMF_2009_49_8_a1,
     author = {V. A. Abilov and M. K. Kerimov},
     title = {Sharp estimates for the convergence rate of double {Fourier} series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1364--1368},
     publisher = {mathdoc},
     volume = {49},
     number = {8},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a1/}
}
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V. A. Abilov; M. K. Kerimov. Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1364-1368. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a1/