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Regular version of the site

Article

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

Functional Analysis and Its Applications. 2017. Vol. 51. No. 2. P. 148-151.
Translator: V. V. Lebedev.

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--P\'al 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.