A variation norm Carleson theorem
- R. Oberlin, A. Seeger, T. Tao, C. Thiele, James Wright
- Mathematics
- 8 October 2009
By a standard approximation argument it follows that S[f ] may be meaningfully defined as a continuous function in ξ for almost every x whenever f ∈ L and the a priori bound of the theorem continues…
A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain
- F. Nazarov, R. Oberlin, C. Thiele
- Mathematics
- 15 December 2009
We introduce a Calderon Zygmund decomposition such that the bad function has vanishing integral against a number of pure frequencies. Then we prove a variation norm variant of a maximal inequality…
A VARIATION
- R. Oberlin, A. Seeger, T. Tao, C. Thiele, J. Wright
- Mathematics
- 2009
By a standard approximation argument it follows that S[f ] may be meaningfully defined as a continuous function in ξ for almost every x whenever f ∈ L and the a priori bound of the theorem continues…
Variation bounds for spherical averages
- David Beltran, R. Oberlin, L. Roncal, A. Seeger, Betsy Stovall
- MathematicsMathematische Annalen
- 15 September 2020
We consider r -variation operators for the family of spherical means, with special emphasis on $$L^p\rightarrow L^q$$ L p → L q estimates.
Discrete inverse problems for Schrödinger and Resistor networks
- R. Oberlin
- Mathematics
For each positive integer n, construct a square graph with boundary Γ = (V, VB, E) as follows. V is the set of vertices in the graph and consists of the integer lattice points (x, y) where 0 ≤ x ≤…
The Kakeya set and maximal conjectures for algebraic varieties over finite fields
- J. Ellenberg, R. Oberlin, T. Tao
- Mathematics
- 10 March 2009
Using the polynomial method of Dvir \cite{dvir}, we establish optimal estimates for Kakeya sets and Kakeya maximal functions associated to algebraic varieties $W$ over finite fields $F$. For…
Sparse Bounds for a Prototypical Singular Radon Transform
- R. Oberlin
- MathematicsCanadian mathematical bulletin
- 13 April 2017
Abstract We use a variant of a technique used by M. T. Lacey to give sparse $L^{p}(\log (L))^{4}$ bounds for a class of model singular and maximal Radon transforms.
New uniform bounds for a Walsh model of the bilinear Hilbert transform
- R. Oberlin, C. Thiele
- Mathematics
- 22 April 2010
We prove old and new $L^p$ bounds for the quartile operator, a Walsh model of the bilinear Hilbert transform, uniformly in the parameter that models degeneration of the bilinear Hilbert transform. We…
Two bounds for the X-ray transform
- R. Oberlin
- Mathematics
- 30 October 2006
We use the arithmetic-combinatorial method of Katz and Tao to give mixed-norm estimates for the X-ray transform on $${\mathbb {R}^d}$$ when d ≥ 4.
Variational bounds for a dyadic model of the bilinear Hilbert transform
- Yen Q. Do, R. Oberlin, E. Palsson
- Mathematics
- 22 March 2012
We prove variation-norm estimates for the Walsh model of the truncated bilinear Hilbert transform, extending related results of Lacey, Thiele, and Demeter. The proof uses analysis on the Walsh phase…
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