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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive
Sib. Èlektron. Mat. Izv., 2019 Volume 16, Pages 85–95 (Mi semr1053)
Real, complex and functional analysis

On the convergence of the Luzin integral and its analogues

K. I. Knizhova, I. V. Podviginba

a Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
b Sobolev Institute of Mathematics, 4, pr. Koptyuga, 630090, Novosibirsk, Russia

Abstract: We study the convergence at a fixed point of the singular integral of Luzin and its analogues. We present sufficient conditions in terms of the Fourier coefficients of the given integrable function for such convergence.

Keywords: trigonometric conjugate function, trigonometric conjugate series, Luzin integral.

UDC: 517.518.454, 517.518.13

MSC: 42A50

Received December 6, 2018, published January 27, 2019

DOI: 10.33048/semi.2019.16.004



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