5 papers
Fourier restriction estimates based on -dimensions: beyond Stein--Tomas
Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana
The well-known Stein--Tomas restriction theorem gives the sharp range of for which restriction estimates hold for the surface measure on the sphere. This was gener…
Knapp-type obstructions in multilinear fractal Fourier extension
Itamar Oliveira, Ana E. de Orellana
For curved, smooth hypersurfaces, the classical Knapp example shows that the Stein--Tomas theorem, which gives linear Fourier restriction estimates, is sharp. Variants of this exam…
Fourier restriction for the additive Brownian sheet
Jonathan M. Fraser, Ana E. de Orellana
The Fourier restriction problem asks when it is meaningful to restrict the Fourier transform of a function to a given set. Many of the key examples are smooth co-dimension 1 manifo…
restriction estimates from the Fourier spectrum
Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana
The Stein--Tomas restriction theorem is an important result in Fourier restriction theory. It gives a range of for which restriction estimates hold for a given mea…
A Fourier analytic approach to exceptional set estimates for orthogonal projections
Jonathan M. Fraser, Ana E. de Orellana
Marstrand's celebrated projection theorem gives the Hausdorff dimension of the orthogonal projection of a Borel set in Euclidean space for almost all orthogonal projections. It is…