## 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… Expand

## 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… Expand

## 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… Expand

## 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 ≤… Expand

## 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… Expand

## 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… Expand

## 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… Expand

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