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arXiv · 1603.04539

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

V. V. Lebedev
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Abstract

It is well--known that certain properties of continuous functions on the circle $\mathbb T$, 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--P\'al theorem. In the present work we provide a short and technically very simple proof of the Jurkat--Waterman theorem. Our approach yields a stronger result.

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V. V. Lebedev. 2016-03-15. A short and simple proof of the Jurkat--Waterman theorem on conjugate functions. https://doi.org/10.1007/s10688-017-0177-0

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