Dindoš M. Hardy spaces and potential theory on C1 domains in Riemannian manifolds. - Providence: AMS,2008. - 78 p. - (Memoirs of the American mathematical society; N 894). - ISSN 0065-9266; ISBN 0821840436  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Abstract ....................................................... vi Chapter 0. Introduction ......................................... 1 Chapter 1. Background and Definitions ........................... 4 §1.1. Notation, terminology and known results ................ 4 §1.2. Hardy spaces and layer potentials ...................... 6 Chapter 2. The Boundary Layer Potentials ........................ 9 §2.1. Compactness of operators К, К* ......................... 9 §2.2. Invertibility of ±½l+K, ±½l+K* ........................ 19 Chapter 3. The Dirichlet problem ............................... 21 §3.1. Lp boundary data ...................................... 21 §3.2. Hardy space boundary data ............................. 23 §3.3. Holder space boundary data ............................ 25 Chapter 4. The Neumann problem ................................. 27 §4.1. Lp boundary data ...................................... 27 §4.2. Hardy space boundary data ............................. 27 §4.3. Holder space boundary data ............................ 29 Chapter 5. Compactness of Layer Potentials, Part II; The Dirichlet regularity problem ............................ 31 §5.1. Preliminaries ......................................... 31 §5.2. Compactness and invertibility of К on Sobolev space H1,р ................................................... 33 §5.3. Compactness and invertibility of К on Hardy-Sobolev space H1,р ............................................. 38 §5.4. Dirichlet regularity problem, Sobolev H1,р(1<p<∞) data .................................................. 41 §5.5. Dirichlet regularity problem, H1,р((n—1)/n<p≤1) data ... 42 Chapter 6. The equivalence of Hardy space definitions .......... 44 §6.1. Preliminaries ......................................... 44 §6.2. C-suharmonicity ....................................... 45 §6.3. The main step ......................................... 47 §6.4. The equivalence theorem on C1 domains ................. 50 §6.5. The equivalence theorem on Lipschitz domains .......... 51 APPENDIX A. Variable Coefficient Cauchy Integrals .............. 53 APPENDIX B. One Result on the Maximal Operator ................. 65 Bibliography ................................................... 77