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

Boris Golubov


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.


Multiple Haar system; Fourier-Haar coefficients; Absolute convergence; $p$th-power Hardy type variation

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