I. V. Limonova, “Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator”, Mat. Sb., 2023, Volume 214, Number 11,Pages <nobr>63

This article is cited in 3 papers

Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator

I. V. Limonova^ab

^a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
^b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: 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

MSC: 42A55

Received: 26.04.2023 and 06.06.2023

DOI: 10.4213/sm9929