Geodesic
Linear summability methods for expansions of functions in the classes $L^p_\mu$ $(1\leqslant p\leqslant\infty)$ in orthonormal systems of polynomial type
Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 709-724

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In this article, sufficient conditions are derived under which, for all $x\in E\subset[a,b]$ (or uniformly on some set $E_1\subset[a,b]$), the following relation holds: $$ \lim_{n\to\infty}U_n(f,x,\Lambda)=f(x), $$ where the $U_n(f,x,\Lambda)$ are linear means of expansions of functions in the classes $L^p_\mu$ $(1\leqslant p\leqslant\infty)$ in orthonormal systems of polynomial type. 
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     author = {B. P. Osilenker},
     title = {Linear summability methods for expansions of functions in the classes $L^p_\mu$ $(1\leqslant p\leqslant\infty)$ in orthonormal systems of polynomial type},
     journal = {Izvestiya. Mathematics },
     pages = {709--724},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a2/}
}
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B. P. Osilenker. Linear summability methods for expansions of functions in the classes $L^p_\mu$ $(1\leqslant p\leqslant\infty)$ in orthonormal systems of polynomial type. Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 709-724. http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a2/