Geometric and Functional Analysis

, Volume 19, Issue 2, pp 429–456

Arithmetic Progressions in Sets of Fractional Dimension

Authors

    • Department of MathematicsUniversity of British Columbia
  • Malabika Pramanik
    • Department of MathematicsUniversity of British Columbia
Article

DOI: 10.1007/s00039-009-0003-9

Cite this article as:
Łaba, I. & Pramanik, M. Geom. Funct. Anal. (2009) 19: 429. doi:10.1007/s00039-009-0003-9

Abstract

Let \({E \subset\mathbb{R}}\) 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.

Keywords and phrases

Arithmetic progressionsSalem setsHausdorff dimensionrestriction estimates

2000 Mathematics Subject Classification

28A7842A3242A3842A4511B25

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009