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

Authors

  • Boris Golubov Department of Higher Mathematics, Moscow Institute of Physics and Technologies, Institute lane 9, 141700, Dolgoproudny, Moscow region

DOI:

https://doi.org/10.26713/cma.v3i3.208

Keywords:

Multiple Haar system, Fourier-Haar coefficients, Absolute convergence, $p$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.

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How to Cite

Golubov, B. (2012). Absolute Convergence of Multiple Series of Fourier-Haar Coefficients of Functions of Bounded $p$th-Power Hardy Type Variation. Communications in Mathematics and Applications, 3(3), 243–252. https://doi.org/10.26713/cma.v3i3.208

Issue

Vol. 3 No. 3 (2012)

Section

Research Article

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