Some Recent Progress on the Restriction Conjecture Page 1 Some Recent Progress on the
Restriction Conjecture Terence Tao Department of Mathematics, UCLA, Los Angeles, CA …

During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …

We prove d-linear analogues of the classical restriction and Kakeya conjectures in R d. Our
approach involves obtaining monotonicity formulae pertaining to a certain evolution of …

The sharp range of L^p-estimates for the class of Hörmander-type oscillatory integral
operators is established in all dimensions under a positive-definite assumption on the …

We consider abstract non-negative self-adjoint operators on L 2 (X) which satisfy the finite-
speed propagation property for the corresponding wave equation. For such operators, we …

Abstract The classical Stein–Tomas restriction theorem is equivalent to the fact that the
spectral measure d “E (λ) of the square root of the Laplacian on ℝ n is bounded from L p (ℝ …

Let T be a linear operator that, for some p1 2. 1; 1/, is bounded on Lp1. Qw/for all Qw 2 Ap1.
Rd/and in addition compact on Lp1. w1/for some w1 2 Ap1. Rd/. Then T is bounded and …

We study the maximal estimates for the bilinear spherical average and the bilinear Bochner-
Riesz operator. First, we obtain L p× L q→ L r estimates for the bilinear spherical maximal …

Recently, the sharp $ L^ 2$-bilinear (adjoint) restriction estimates for the cone and the
paraboloid were established by Wolff and Tao, respectively. Their results rely on the fact that …

Given a fixed p≠ 2, we prove a simple and effective characterization of all radial multipliers
of FL^p\left(R^d\right), provided that the dimension d is sufficiently large. The method also …