S. S. Volosivets, “Absolute convergence of single and double Fourier series on multiplicative systems”, Izv. Saratov Univ. Math. Mech. Inform., 2009, Volume 9, Issue 3,Pages <nobr>7

Mathematics

Absolute convergence of single and double Fourier series on multiplicative systems

S. S. Volosivets

Saratov State University, Chair of Theory of Functions and Approximations

Abstract: Two-dimensional analogs of famous Zygmund and Szasz tests for absolute convergence of Fourier–Vilenkin series are established. Also it is proved that two-dimensional Szasz test is the best possible in the certain sense.

Key words: absolute convergence, Fourier–Vilenkin series, modulus of continuity, functions of bounded $p$-fluctuation.

UDC: 517.518

DOI: 10.18500/1816-9791-2009-9-3-7-14