arXiv subjects

Terence Tao

Publications and source records attributed to Terence Tao.

344 records · Page 20Linked to original sources

arXiv1998

A bilinear approach to the restriction and Kakeya conjectures

Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the $(L^p,L^p)$ spherical restriction theorem of Wolff from $p > 42/11$ to $p > 34/9$, and also obtain a sharp $(L^p,L^q)$ spherical restriction theorem for $q > 4 - 5/27$.

math.CA↗

arXiv1997

Low regularity semi-linear wave equations

We prove local well-posedness results for the semi-linear wave equation for data in $H^γ$, $0 < γ< \frac{n-3}{2(n-1)}$, extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space $X^{r,p}_k$.

math.AP↗