276 citations · 4.5k across the 293 of their papers we have counts for
11 papers · 2 filters
L^p bounds for a maximal dyadic sum operator
Loukas Grafakos, Terence Tao, Erin Terwilleger
We prove bounds in the range for a maximal dyadic sum operator on $\rn$. This maximal operator provides a discrete multidimensional model of Carleson's operator.…
A sharp bilinear restriction estimate for paraboloids
Terence Tao
Recently Wolff obtained a sharp bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets…
Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} times R
Adam Sikora, Terence Tao
We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E_{Delta_{S^{2m-1}}}([0,R)) are uniformly bounded as an operator from H^p(S^{2m-1}) to…
Singular maximal functions and Radon transforms near L^1
Andreas Seeger, Terence Tao, James Wright
We show that some singular maximal functions and singular Radon transforms satisfy a weak type inequality. Examples include the maximal function and Hilbert transform…
Pointwise convergence of lacunary spherical means
Andreas Seeger, Terence Tao, James Wright
We show that if is locally in then the lacunary spherical means converge almost everywhere. The argument given here is a model case for more general results on si…
Endpoint mapping properties of spherical maximal operators
Andreas Seeger, Terence Tao, James Wright
For a function , , let be the mean of over the sphere of radius centered at . Given a set of dilations we pr…
A Carleson type theorem for a Cantor group model of the scattering transform
Camil Muscalu, Terence Tao, Christoph Thiele
We consider a basic -adic model for the scattering transform on the line. We prove bounds for this scattering transform and a weak bound for a Carleson type maximal…
A new bound for finite field Besicovitch sets in four dimensions
Terence Tao
Let be a finite field with characteristic greater than two. Define a \emph{Besicovitch set} in to be a set containing a line in every direction. The \em…
Restriction and Kakeya phenomena for finite fields
Gerd Mockenhaupt, Terence Tao
The restriction and Kakeya problems in Euclidean space have received much attention in the last few decades, and are related to many problems in harmonic analysis, PDE, and number…
On the bi-carleson operator I. The Walsh case
Camil Muscalu, Terence Tao, Christoph Thiele
We prove estimates for the Walsh model of the maximal bi-Carleson operator (which is a hybrid of the bilinear Hilbert transform and the Carleson maximal operator which appear…
The weak-type of Fourier integral operators of order
Terence Tao
Let be a Fourier integral operator on of order . It was shown by Seeger, Sogge, and Stein that mapped the Hardy space to . In this note we show…