Abstract:
For orthogonal systems of Haar type introduced by N.Ya. Vilenkin in 1958 we study absolute convergence of series from Fourier coefficients raised to a positive power with multiplicators from Gogoladze–Meskhia class. The conditions for convergence of the series mentioned above are given in terms of best approximations of functions in LpLp spaces by polynomials with respect to Haar type systems or in terms of fractional modulus of continuity of functions from Wiener spaces VpVp, p>1p>1. We establish the sharpness of obtained results.
Keywords:
Haar type system, Fourier coefficients, LpLp space, functions of bounded pp-variation, best approximation, modulus of continuity.
Citation:
S. S. Volosivets, B. I. Golubov, “Generalized absolute convergence of series from Fourier coeficients by systems of Haar type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 1, 10–20; Russian Math. (Iz. VUZ), 62:1 (2018), 7–16
\Bibitem{VolGol18}
\by S.~S.~Volosivets, B.~I.~Golubov
\paper Generalized absolute convergence of series from Fourier coeficients by systems of Haar type
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 1
\pages 10--20
\mathnet{http://mi.mathnet.ru/ivm9314}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 1
\pages 7--16
\crossref{https://doi.org/10.3103/S1066369X18010024}
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https://www.mathnet.ru/eng/ivm9314
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This publication is cited in the following 2 articles:
G. Cagareishvili, L. Gogoladze, “General Fourier coefficients for lip alpha class functions”, Acta Math. Hung., 161:1 (2020), 327–340
V. I. Filippov, “Series of Fourier type with integer coefficients by systems of dilates and translates of one function in LpLp, p≥1p≥1”, Russian Math. (Iz. VUZ), 63:6 (2019), 51–57
Citation in format AMSBIB
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