The well-known Bohr-Pál theorem asserts that for every continuous real-valued function f on the circle there exists a change of variable, i.e., a homeomorphism h of onto itself, such that the Fourier series of the superposition f ∘ h converges uniformly. Subsequent improvements of this result imply that actually there exists a homeomorphism that brings f into the Sobolev space . This refined version of the Bohr-Pál theorem does not extend to complex-valued functions. We show that if α < 1/2, then there exists a complex-valued f that satisfies the Lipschitz condition of order α and at the same time has the property that for every homeomorphism h of .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8438-1-2016,
author = {Vladimir Lebedev},
title = {The Bohr-Pal theorem and the Sobolev space $W2^{1/2}$
},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {73-81},
zbl = {06545410},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8438-1-2016}
}
Vladimir Lebedev. The Bohr-Pál theorem and the Sobolev space $W₂^{1/2}$
. Studia Mathematica, Tome 231 (2015) pp. 73-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8438-1-2016/