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10 papers · 1 filter
Extension Theorems for Paraboloids in the Finite Field Setting
Alex Iosevich, Doowon Koh
In this paper we study the boundedness of the extension operators associated with paraboloids in vector spaces over finite fields.In higher even dimensions, we estimate t…
Distances sets that are a shift of the integers and Fourier basis for planar convex sets
Alex Iosevich, Philippe Jaming
The aim of this paper is to prove that if a planar set has a difference set satisfying for suitable than has at most 3 elements. This result…
Geometric incidence theorems via Fourier analysis
A. Iosevich, H. Jorati, I. Laba
We prove that non-trivial bounds for generalized Radon transforms imply correspondingly non-trivial discrete incidence theorems for manifolds and suitably regular point sets.
Dahlberg's bilinear estimate for solutions of divergence form complex elliptic equations
S. Hofmann
We consider divergence form elliptic operators $L=-\dv A(x)\nabla$, defined in , where the coeff…
Ubiquity of simplices in subsets of vector spaces over finite fields
Derrick Hart, Alex Iosevich
We prove that a sufficiently large subset of the -dimensional vector space over a finite field with elements, , contains a copy of every -simplex. Fourier…
On singular integral and martingale transforms
S. Geiss, S. Montgomery-Smith, E. Saksman
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant o…