Fourier series in BMO with number theoretical implications

We introduce an elementary argument to bound the BMO seminorm of Fourier series with gaps giving in particular a sufficient condition for them to be in this space. Using finer techniques we carry out a detailed study of the series ∑ n - 1 e 2 π i n 2 x providing some insight into how much this BMO F...

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Bibliographic Details
Published inMathematische annalen Vol. 376; no. 1-2; pp. 457 - 473
Main Authors Chamizo, Fernando, Córdoba, Antonio, Ubis, Adrián
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2020
Springer Nature B.V
Subjects
Fourier series
Mathematics
Mathematics and Statistics
30H35
42A32
30H10
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Summary:We introduce an elementary argument to bound the BMO seminorm of Fourier series with gaps giving in particular a sufficient condition for them to be in this space. Using finer techniques we carry out a detailed study of the series ∑ n - 1 e 2 π i n 2 x providing some insight into how much this BMO Fourier series differs from defining an L ∞ function.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-019-01882-9