Geodesic
Conservative Means of Orthogonal Series and the Spaces $L^p[0;1]$, $p\in (1;\infty )$
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 182-193

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Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space $L^p[0;1]$, $p\in (1;\infty )$, are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki. 
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     author = {I. N. Brui},
     title = {Conservative {Means} of {Orthogonal} {Series} and the {Spaces} $L^p[0;1]$, $p\in (1;\infty )$},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a2/}
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I. N. Brui. Conservative Means of Orthogonal Series and the Spaces $L^p[0;1]$, $p\in (1;\infty )$. Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 182-193. http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a2/