Arithmetic Progressions in Sets of Fractional Dimension

Let be a closed set of Hausdorff dimension α . Weprove that if α is sufficiently close to 1, and if E supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then E contains non-trivial 3-term arithmetic progressions.

Saved in:
Bibliographic Details
Published inGeometric and functional analysis Vol. 19; no. 2; pp. 429 - 456
Main Authors Łaba, Izabella, Pramanik, Malabika
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.09.2009
Subjects
Analysis
Mathematics
Mathematics and Statistics
Salem sets
42A45
Arithmetic progressions
Hausdorff dimension
42A32
28A78
42A38
11B25
restriction estimates
Online AccessGet full text

Cover

More Information
Summary:Let be a closed set of Hausdorff dimension α . Weprove that if α is sufficiently close to 1, and if E supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then E contains non-trivial 3-term arithmetic progressions.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-009-0003-9