11 citations · 32 across the 12 of their papers we have counts for
15 papers
Oscillatory integral operators and variable Schrödinger propagators: beyond the universal estimates
Mingfeng Chen, Shengwen Gan, Shaoming Guo +3
We consider a class of Hörmander-type oscillatory integral operators in for odd with real analytic phase. We derive weak conditions on the phase which ens…
On integer distance sets
Rachel Greenfeld, Marina Iliopoulou, Sarah Peluse
We develop a new approach to address some classical questions concerning the size and structure of integer distance sets. Our main result is that any integer distance set in the Eu…
Some sharp inequalities of Mizohata--Takeuchi-type
Anthony Carbery, Marina Iliopoulou, Hong Wang
Let be a strictly convex, compact patch of a hypersurface in , with non-vanishing Gaussian curvature and surface measure induced by the Lebesgue measur…
Sharp estimates for oscillatory integral operators of arbitrary signature
Jonathan Hickman, Marina Iliopoulou
The sharp range of -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a general signature assumption on the phase…
Joints formed by lines and a -plane, and a discrete estimate of Kakeya type
Anthony Carbery, Marina Iliopoulou
Let be a family of lines and let be a family of -planes in where is a field. In our first result we show that the number…
Inequalities of Riesz-Sobolev type for compact connected Abelian groups
Michael Christ, Marina Iliopoulou
A version of the Riesz-Sobolev convolution inequality is formulated and proved for arbitrary compact connected Abelian groups. Maximizers are characterized and a quantitative stabi…
Sharp estimates for oscillatory integral operators via polynomial partitioning
Larry Guth, Jonathan Hickman, Marina Iliopoulou
The sharp range of -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase…
A multilinear Fourier extension identity on
Jonathan Bennett, Marina Iliopoulou
We prove an elementary multilinear identity for the Fourier extension operator on , generalising to higher dimensions the classical bilinear extension identity in the…
A sharp -plane Strichartz inequality for the Schrödinger equation
Jonathan Bennett, Neal Bez, Taryn C. Flock +2
We prove that where is the solution to the linear time-dependent Schrödinger equation on …
Incidence bounds on multijoints and generic joints
Marina Iliopoulou
A point is a joint formed by a finite collection of lines in if there exist at least lines in through that…
Flow monotonicity and Strichartz inequalities
Jonathan Bennett, Neal Bez, Marina Iliopoulou
We identify complete monotonicity properties underlying a variety of well-known sharp Strichartz inequalities in euclidean space.
Counting joints in vector spaces over arbitrary fields
Anthony Carbery, Marina Iliopoulou
We give a proof of the "folklore" theorem that the Kaplan--Sharir--Shustin/Quilodrán result on counting joints associated to a family of lines holds in vector spaces over arbitrary…
Counting multijoints
Marina Iliopoulou
Let , , be finite collections of , , , respectively, lines in , and $J(\mathfrak{L}_1, \mathfrak{L}_2,…
Discrete analogues of Kakeya problems
Marina Iliopoulou
This thesis investigates two problems that are discrete analogues of two harmonic analytic problems which lie in the heart of research in the field. More specifically, we consider…
Counting joints with multiplicities
Marina Iliopoulou
Let be a collection of lines in and the set of joints formed by , i.e. the set of points each of which lies in at least 3 non-coplanar l…