Geodesic
Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 966-980

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Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space $L_2((a,b),p(x))$. Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered. 
@article{ZVMMF_2009_49_6_a3,
     author = {V. A. Abilov and F. V. Abilova and M. K. Kerimov},
     title = {Sharp estimates for the convergence rate of {Fourier} series in terms of orthogonal polynomials in $L_2((a,b),p(x))$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {966--980},
     publisher = {mathdoc},
     volume = {49},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a3/}
}
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V. A. Abilov; F. V. Abilova; M. K. Kerimov. Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 966-980. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a3/