Thomas Wolff

An improved bound for Kakeya type maximal functions

The purpose of this paper is to improve the known results (specifically [1]) concerning Lp boundedness of maximal functions formed using 1 x d x ... x d tubes.

A sharp bilinear cone restriction estimate

The purpose of this paper is to prove an essentially sharp L^2 Fourier restriction estimate for light cones, of the type which is called bilinear in the recent literature.

Lectures on Harmonic Analysis

The

A local smoothing estimate in higher dimensions

L^1

On the Steinhaus tiling problem

Fourier transform The Schwartz space Fourier inversion and the Plancherel theorem Some specifics, and

A KAKEYA-TYPE PROBLEM FOR CIRCLES

L^p

Lifshitz tails for 2-dimensional random Schrödinger operators

for

Unique Continuation with Weak Type Lower Order Terms

p<2

On peak sets for Lip α classes

The uncertainty principle The stationary phase method The restriction problem Hausdorff measures Sets with maximal Fourier dimension and distance sets The Kakeya problem Recent work connected with the Kakeya problem Bibliography for Chapter 11 Historical notes Bibliography.

Appendix tosome harmonic analysis questions suggested by anderson-bernoulli models: A general contraction property in PSL(2, ℝ)

We prove the higher-dimensional analogue of Wolffs local smoothing estimate (Geom. Funct. Anal. 2001) for large p. As in the 2+1-dimensional case, the estimate is sharp for any given value of p, but it is likely that the range of p can be improved.