A MASS TRANSFERENCE PRINCIPLE AND SETS WITH LARGE INTERSECTIONS
Persson, Tomas LU
(2022)
In Real Analysis Exchange
47(1).
p.191-206
- Abstract
I prove a mass transference principle for general shapes, similar to a recent result by H. Koivusalo and M. Rams. The proof relies on Vitali's covering lemma and manipulations with Riesz energies. The main novelty is that it is proved that the obtained limsup-set belongs to the classes of sets with large intersections, as defined by K. Falconer. This has previously not been proved for as general shapes as in this paper.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/c1dc8914-3e46-4e58-a69e-51978d253668
- author
- Persson, Tomas
LU
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Hausdorff dimension, Mass transference principle
- in
- Real Analysis Exchange
- volume
- 47
- issue
- 1
- pages
- 16 pages
- publisher
- Michigan State University Press
- external identifiers
-
- scopus:85134307310
- ISSN
- 0147-1937
- DOI
- 10.14321/realanalexch.47.1.1619498208
- language
- English
- LU publication?
- yes
- id
- c1dc8914-3e46-4e58-a69e-51978d253668
- date added to LUP
- 2022-10-11 10:09:36
- date last changed
- 2022-10-11 10:09:36
@article{c1dc8914-3e46-4e58-a69e-51978d253668,
abstract = {{<p>I prove a mass transference principle for general shapes, similar to a recent result by H. Koivusalo and M. Rams. The proof relies on Vitali's covering lemma and manipulations with Riesz energies. The main novelty is that it is proved that the obtained limsup-set belongs to the classes of sets with large intersections, as defined by K. Falconer. This has previously not been proved for as general shapes as in this paper.</p>}},
author = {{Persson, Tomas}},
issn = {{0147-1937}},
keywords = {{Hausdorff dimension; Mass transference principle}},
language = {{eng}},
number = {{1}},
pages = {{191--206}},
publisher = {{Michigan State University Press}},
series = {{Real Analysis Exchange}},
title = {{A MASS TRANSFERENCE PRINCIPLE AND SETS WITH LARGE INTERSECTIONS}},
url = {{http://dx.doi.org/10.14321/realanalexch.47.1.1619498208}},
doi = {{10.14321/realanalexch.47.1.1619498208}},
volume = {{47}},
year = {{2022}},
}