Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 2, pp. 247-275 (2016)

On various types of continuity of multiple dyadic integrals

Mikhail Plotnikov and Valentin Skvortsov

Moscow State University, Casimirus the Great University, and Vologda State Milk Industry Academy

Abstract: The paper presents a survey of results related to continuity properties of dyadic integrals used in solving the problem of recovering, by generalized Fourier formulas, the coefficients of series with respect to multiple Haar and Walsh systems.

Keywords: Perron dyadic integral, Saks continuity, chessboard continuity, dyadic group, Walsh series, Haar series, rectangular convergence, sets of uniqueness, quasi-measure

Classification (MSC2000): 26A39; 42C10

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