Eswarathasan, Suresh, Iosevich, Alex and Taylor, Krystal 2016. Intersections of sets and Fourier analysis. Journal d'Analyse Mathématique 128 , pp. 159-178. 10.1007/s11854-016-0004-1 |
Preview |
PDF
- Accepted Post-Print Version
Download (170kB) | Preview |
Abstract
A classical theorem due to Mattila says that if A, B ⊂ ℝ d of Hausdorff dimension s A , s B respectively with s A + s B ≥ d, s B > (d + 1)/2, and dim H (A × B) = s A + s B ≥ d, then dimH(A∩(z+B)⩽sA+sB−d dimH(A∩(z+B)⩽sA+sB−d for almost every z ∈ ℝ d , in the sense of Lebesgue measure. In this paper, we replace the Hausdorff dimension on the left hand side of the first inequality above by the lower Minkowski dimension and replace the Lebesgue measure of the set of translates by a Hausdorff measure on a set of sufficiently large dimension. Interesting arithmetic issues arise in the consideration of sharpness examples.
Item Type: | Article |
---|---|
Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Additional Information: | Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0021-7670/ (accessed 22/06/2016) |
Publisher: | Springer Verlag (Germany) |
ISSN: | 0021-7670 |
Date of First Compliant Deposit: | 30 March 2016 |
Last Modified: | 06 Nov 2023 23:36 |
URI: | https://orca.cardiff.ac.uk/id/eprint/86431 |
Citation Data
Cited 1 time in Scopus. View in Scopus. Powered By Scopus® Data
Actions (repository staff only)
Edit Item |