|
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.
Received December 6, 2018, published January 27, 2019
Citation:
K. I. Knizhov, I. V. Podvigin, “On the convergence of the Luzin integral and its analogues”, Sib. Èlektron. Mat. Izv., 16 (2019), 85–95
Linking options:
https://www.mathnet.ru/eng/semr1053 https://www.mathnet.ru/eng/semr/v16/p85
|
Statistics & downloads: |
Abstract page: | 323 | Full-text PDF : | 174 | References: | 38 |
|