Absolute Convergence of Multiple Series of Fourier-Haar Coefficients of Functions of Bounded p th -Power Hardy Type Variation

Abstract

For functions of two variables having bounded $p$th-power variation of Hardy type on unit square the sufficient condition for absolute convergence of double series of Fourier-Haar coefficients with power type weights is obtained. From this condition we obtain two corollaries for absolute convergence of the series of Fourier-Haar coefficients of functions of one variable of bounded Wiener $p$th-power variation or belonging to the class Lip $\alpha$. The main result and all corollaries are sharp. $N$-dimensional analogs of main result and corollaries are formulated.