Integrability of orthogonal projections, and applications to Furstenberg sets

Damian Dąbrowski, Tuomas Orponen, Michele Villa

Type: Article

Publication Date: 2022-07-15

Citations: 6

DOI: https://doi.org/10.1016/j.aim.2022.108567

View Publication

Locations

Advances in Mathematics - View
arXiv (Cornell University) - View - PDF
University of Oulu Repository (University of Oulu) - View - PDF
Jyväskylä University Digital Archive (University of Jyväskylä) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Integrability of orthogonal projections, and applications to Furstenberg sets	2021	Damian Dąbrowski Tuomas Orponen Michele Villa
+	On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane	2021	Tuomas Orponen Pablo Shmerkin
+ PDF Chat	On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane	2023	Tuomas Orponen Pablo Shmerkin
+	Furstenberg sets estimate in the plane	2023	Kevin Ren Hong Wang
+	Projections, Furstenberg sets, and the $ABC$ sum-product problem	2023	Tuomas Orponen
+ PDF Chat	A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin	2024	Jacob B. Fiedler Guo-Dong Hong Donggeun Ryou Shukun Wu
+ PDF Chat	Hausdorff dimension of unions of affine subspaces and of Furstenberg-type sets	2019	Kornélia Héra Tamás Keleti András Máthé
+	Discretized Radial Projections in $\mathbb{R}^d$	2023	Kevin Ren
+	Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces	2019	Kornélia Héra
+ PDF Chat	An improved bound on the packing dimension of Furstenberg sets in the plane	2019	Tuomas Orponen
+	Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem	2022	Pablo Shmerkin Sheng Wang
+	Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces	2018	Kornélia Héra
+	Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces	2018	Kornélia Héra
+	On the packing dimension of Furstenberg sets	2020	Pablo Shmerkin
+	An improved bound on the packing dimension of Furstenberg sets in the plane	2016	Tuomas Orponen
+	Hausdorff dimension of unions of affine subspaces and of Furstenberg-type sets	2017	Kornélia Héra T Keleti András Máthé
+	An improved bound on the packing dimension of Furstenberg sets in the plane	2016	Tuomas Orponen
+	Kaufman and Falconer estimates for radial projections and a continuum version of Beck's Theorem	2022	Tuomas Orponen Pablo Shmerkin Sheng Wang
+	Projections of planar sets in well-separated directions	2016	Tuomas Orponen
+	Hausdorff dimension of intersections with planes and general sets	2021	Pertti Mattila

Works That Cite This (5)

Action	Title	Year	Authors
+ PDF Chat	On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane	2023	Tuomas Orponen Pablo Shmerkin
+ PDF Chat	Dimensions of Furstenberg sets and an extension of Bourgain’s projection theorem	2024	Pablo Shmerkin Hong Wang
+	Kaufman and Falconer Estimates for Radial Projections and a Continuum Version of Beck’s Theorem	2024	Tuomas Orponen Pablo Shmerkin Hong Wang
+ PDF Chat	Dimension estimates on circular (s,t)-Furstenberg sets	2023	Jiayin Liu
+ PDF Chat	On the discretised ABC sum-product problem	2023	Tuomas Orponen

Works Cited by This (36)

Action	Title	Year	Authors
+ PDF Chat	Recent work connected with the Kakeya problem	2003	Thomas Wolff
+	Fourier Analysis and Hausdorff Dimension	2015	Pertti Mattila
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+ PDF Chat	An X-ray transform estimate in $\mathbb R^n$	2001	Izabella Łaba Terence Tao
+	Classical Fourier Analysis	2014	Loukas Grafakos
+ PDF Chat	On the number of sums and products	1997	György Elekes
+ PDF Chat	$L^{p}$ estimates for the $X$-ray transform	1983	S.W. Drury
+ PDF Chat	Furstenberg sets and Furstenberg schemes over finite fields	2016	Jordan S. Ellenberg Daniel Erman
+ PDF Chat	Polynomials with dense zero sets and discrete models of the Kakeya conjecture and the Furstenberg set problem	2016	Ruixiang Zhang
+	Estimates for singular radon transforms and pseudodifferential operators with singular symbols	1990	Allan Greenleaf Günther Uhlmann