Thickness conditions and Littlewood-Paley sets
We consider sets in the real line that have Littlewood-Paley properties LP(p) or LP and study the following question: How thick can these sets be?
The Bohr-Pál theorem and the Sobolev space
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,...
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