Geodesic
Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator
Sbornik. Mathematics, Tome 214 (2023) no. 11, pp. 1560-1584

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It is shown that any finite orthogonal system of functions whose norms in $L_p$ are bounded by 1, where $p>2$, has a sufficiently dense subsystem with lacunarity property in the Orlicz space. The norm of the maximal partial sum operator for this subsystem has a better estimate than it is guaranteed by the classical Menshov-Rademacher theorem for general orthogonal systems. Bibliography: 17 titles.
Keywords: lacunary subsystems, maximal partial sum operator, Orlicz space 
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     author = {I. V. Limonova},
     title = {Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator},
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I. V. Limonova. Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator. Sbornik. Mathematics, Tome 214 (2023) no. 11, pp. 1560-1584. http://geodesic.mathdoc.fr/item/SM_2023_214_11_a2/