On \(L^p\)-integrability of a special double sine series formed by its blocks. (English) Zbl 1364.42004
J. Contemp. Math. Anal., Armen. Acad. Sci. 52, No. 1, 48-53 (2017); translation from Izv. Nats. Akad. Nauk Armen., Mat. 52, No. 1, 59-67 (2017).
Summary: In this paper we deal with a special double sine trigonometric series formed by its blocks. This type of trigonometric series is of particular interest since its blocks always are bounded, that is, under some additional assumptions the sum-function of such series always exists. We give some conditions under which such sum-function is integrable of power \(p\in\{2, 3, \dots\}\), as well as is integrable with some natural weight.
MSC:
| 42A24 | Summability and absolute summability of Fourier and trigonometric series |
| 42A16 | Fourier coefficients, Fourier series of functions with special properties, special Fourier series |
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
References:
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