Lacey M. On a conjecture of E.M. Stein on the Hilbert transform on vector fields / M.Lacey, X.Li. - Providence: American Mathematical Society, 2010. - viii, 72 p.: ill. - (Memoirs of the American mathematical society; vol.205, N 965). - Ref.: p.71-72. - ISBN 978-0-8218-4540-0; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Chapter 1. Overview of principal results ........................ 1 Chapter 2. Besicovitch set and Carleson's Theorem ............... 7 Besicovitch set ................................................. 7 The Kakeya maximal function ..................................... 8 Carleson's Theorem .............................................. 8 The weak L2 estimate in Theorem 1.15 is sharp ................... 9 Chapter 3. The Lipschitz Kakeya maximal function ............... 11 The weak L2 estimate ........................................... 11 An obstacle to an Lp estimate, for 1 < p < 2 ................... 20 Bourgain's geometric condition ................................. 21 Vector fields that are a function of one variable .............. 24 Chapter 4. The L2 estimate ..................................... 27 Definitions and principal Lemmas ............................... 27 Truncation and an alternate model sum .......................... 31 Proofs of Lemmata .............................................. 34 Chapter 5. Almost orthogonality between annuli ................. 51 Application of the Fourier localization Lemma .................. 51 The Fourier localization estimate .............................. 64 References ..................................................... 71