Abstract:
In this paper, we introduce the concept of a variational modulus of continuity for functions of several
variables, give an estimate for the sum of the coefficients of a multiple Fourier-Haar series in terms of the
variational modulus of continuity, and prove theorems of absolute convergence of series composed of the
coefficients of multiple Fourier-Haar series. In this paper, we study the issue of the absolute convergence
for multiple series composed of the Fourier-Haar coefficients of functions of several variables of bounded
p-variation. We estimate the coefficients of a multiple Fourier-Haar series in terms of the variational
modulus of continuity and prove the sufficiency theorem for the condition for the absolute convergence
of series composed of the Fourier-Haar coefficients of the considered function class. This paper researches
the question: under what conditions, imposed on the variational modulus of continuity of the fractional
order of several variables functions, there is the absolute convergence for series composed of the coefficients
of multiple Fourier-Haar series.
