6 papers
On the parabolic Hausdorff dimension of orthogonal projections
Terence L. J. Harris, Pertti Mattila
For Borel sets we prove lower bounds for the parabolic Hausdorff dimension of the orthogonal projections of on generic -dimensional…
Maximal inequalities and the decay of Fourier transforms of measures
Terence L. J. Harris
It is shown that Schrödinger maximal inequalities over fractals are equivalent to the decay rates of Fourier transforms of fractal measures over the paraboloid. A similar con…
Fourier dimension of the cone
Terence L. J. Harris
It is shown that the cone in has Fourier dimension . This verifies a conjecture of Fraser and Kroon.
An a.e. lower bound for Hausdorff dimension under vertical projections in the Heisenberg group
Terence L. J. Harris
An improved a.e. lower bound is given for Hausdorff dimension under vertical projections in the first Heisenberg group.
Improved decay of conical averages of the Fourier transform
Terence L. J. Harris
An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension . The proof uses a weighted version of the br…
Refined Strichartz inequalities for the wave equation
Terence L. J. Harris
Some analogues of the Schrödinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. These are used to improve the best known fracta…