Fourier Analysis and Hausdorff Dimension (Hardcover)

Preface; Acknowledgements; 1. Introduction; 2. Measure theoretic preliminaries; 3. Fourier transforms; 4. Hausdorff dimension of projections and distance sets; 5. Exceptional projections and Sobolev dimension; 6. Slices of measures and intersections with planes; 7. Intersections of general sets and measures; 8. Cantor measures; 9. Bernoulli convolutions; 10. Projections of the four-corner Cantor set; 11. Besicovitch sets; 12. Brownian motion; 13. Riesz products; 14. Oscillatory integrals (stationary phase) and surface measures; 15. Spherical averages and distance sets; 16. Proof of the Wolff?Erdo?an Theorem; 17. Sobolev spaces, Schrodinger equation and spherical averages; 18. Generalized projections of Peres and Schlag; 19. Restriction problems; 20. Stationary phase and restriction; 21. Fourier multipliers; 22. Kakeya problems; 23. Dimension of Besicovitch sets and Kakeya maximal inequalities; 24. (n, k) Besicovitch sets; 25. Bilinear restriction; References; List of basic notation; Author index; Subject index.