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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 2, Pages 87–91 (Mi faa3440)

Brief communications

A short and simple proof of the Jurkat–Waterman theorem on conjugate functions

V. V. Lebedev

National Research University Higher School of Economics, Moscow, Russia

Abstract: It is well known that certain properties of continuous functions on the circle T related to the Fourier expansion can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the results in this area is the Jurkat–Waterman theorem on conjugate functions, which improves the classical Bohr–Pál theorem. In the present work we propose a short and technically very simple proof of the Jurkat–Waterman theorem. Our approach yields a stronger result.

Keywords: Fourier series, superposition operators, conjugate functions.

DOI: https://doi.org/10.4213/faa3440

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English version:
Functional Analysis and Its Applications, 2017, 51:2, 148–151

Bibliographic databases:

UDC: 517.51
Accepted:19.01.2016

Citation: V. V. Lebedev, “A short and simple proof of the Jurkat–Waterman theorem on conjugate functions”, Funktsional. Anal. i Prilozhen., 51:2 (2017), 87–91; Funct. Anal. Appl., 51:2 (2017), 148–151

Citation in format AMSBIB
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