Geodesic
Generalized absolute convergence of series from Fourier coeficients by systems of Haar type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 10-20

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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 $L^p$ spaces by polynomials with respect to Haar type systems or in terms of fractional modulus of continuity of functions from Wiener spaces $V_p$, $p>1$. We establish the sharpness of obtained results.
Keywords: Haar type system, $L^p$ space, functions of bounded $p$-variation, best approximation, modulus of continuity.
Mots-clés : Fourier coefficients 
@article{IVM_2018_1_a1,
     author = {S. S. Volosivets and B. I. Golubov},
     title = {Generalized absolute convergence of series from {Fourier} coeficients by systems of {Haar} type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--20},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_1_a1/}
}
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S. S. Volosivets; B. I. Golubov. Generalized absolute convergence of series from Fourier coeficients by systems of Haar type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 10-20. http://geodesic.mathdoc.fr/item/IVM_2018_1_a1/