Absolute convergence of double series of Fourier-Haar coefficients for functions of bounded p-variation

Abstract

We consider functions of two variables of bounded p-variation of the Hardy type on the unit square. For these functions we obtain a sufficient condition for the absolute convergence of series of positive powers of Fourier coefficients with power-type weights with respect to the double Haar system. This condition implies those for the absolute convergence of series of Fourier-Haar coefficients of one-variable functions which have a bounded Wiener p-variation or belong to the class Lip α. We show that the obtained results are unimprovable. We also formulate N-dimensional analogs of the main result and its corollaries.