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Thickness conditions and Littlewood-Paley sets

100%

Lebedev V.

Studia Mathematica

2014

tom 220

nr 3

265-276

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 $W₂^{1/2}$

100%

Lebedev V.

Studia Mathematica

2015

tom 231

nr 1

73-81

The well-known Bohr-Pál theorem asserts that for every continuous real-valued function f on the circle 𝕋 there exists a change of variable, i.e., a homeomorphism h of 𝕋 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 $W₂^{1/2}(𝕋)$. 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 $f ∘ h ∉ W₂^{1/2}(𝕋)$ for every homeomorphism h of 𝕋.

Ograniczanie wyników

2 Studia Mathematica

2 Lebedev V.

1 2015

1 2014

Wyniki wyszukiwania

Thickness conditions and Littlewood-Paley sets

The Bohr-Pál theorem and the Sobolev space $W₂^{1/2}$