Affiliation:
1. Department of Mathematics and Statistics University of Helsinki Helsinki Finland
Abstract
AbstractThis paper extends some results of Mattila (J. Fractal Geom. 66 (2021) 389–401 and Ann. Acad. Sci. Fenn. A Math. 42 (2017) 611–620), in particular, removing assumptions of positive lower density. We give conditions on a general family , of orthogonal projections which guarantee that the Hausdorff dimension formula holds generically for measurable sets with positive and finite ‐dimensional Hausdorff measure, . As an application we prove for Borel sets with positive ‐ and measures that if , then for almost all rotations and for positively many . We shall also give an application to the estimates of the dimension of the set of exceptional rotations.
Reference17 articles.
1. Sharp L2$L^2$ estimates of the Schrödinger maximal function in higher dimensions;Zhang X. Du and R.;Ann. of Math.,2019
2. Classes of sets with large intersection
3. On Falconer’s distance set problem in the plane
4. A Euclidean Fourier‐analytic approach to vertical projections in the Heisenberg group
5. T. L. J.Harris AnL4/3$L^{4/3}$SL2$SL_2$Kakeya maximal inequality arXiv:2311.14667.