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On the order of magnitude of Walsh-Fourier transform. (English) Zbl 1499.42153

Behavior of the classical Fourier transform for functions of bounded variation is well studied both in dimension one and in several dimensions. It is worth mentioning that a massive study of the Fourier transforms for functions of bounded variation is taken in reviewer’s book [Functions of bounded variation and their Fourier transforms. Cham: Birkhäuser (2019; Zbl 1418.42001)]. See also the recent paper [M. Okada and Y. Sawano, J. Fourier Anal. Appl. 27, No. 2, Paper No. 23, 31 p. (2021; Zbl 1475.42014)], and references in both sources. In the paper under review, the authors transfer this study to the case of the Walsh-Fourier transform.

MSC:

42C20 Other transformations of harmonic type
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
26A45 Functions of bounded variation, generalizations
26B30 Absolutely continuous real functions of several variables, functions of bounded variation
26D15 Inequalities for sums, series and integrals
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