Hardy Spaces and Potential Theory on C^{1} Domains in Riemannian Manifolds.

Intro -- Contents -- Abstract -- Chapter 0. Introduction -- Chapter 1. Background and Definitions -- 1.1. Notation, terminology and known results -- 1.2. Hardy spaces and layer potentials -- Chapter 2. The Boundary Layer Potentials -- 2.1. Compactness of operators K, K* -- 2.2. Invertibility of ±1/2+ K, ±1/2 + K* -- Chapter 3. The Dirichlet problem -- 3.1. L[sup(p)] boundary data -- 3.2. Hardy space boundary data -- 3.3. Holder space boundary data -- Chapter 4. The Neumann problem -- 4.1. L[sup(p)] boundary data -- 4.2. Hardy space boundary data -- 4.3. Holder space boundary data -- Chapter 5. Compactness of Layer Potentials, Part II -- The Dirichlet regularity problem -- 5.1. Preliminaries -- 5.2. Compactness and invertibihty of K on Sobolev space H[sup(1,p)] -- 5.3. Compactness and invertibihty of K on Hardy-Sobolev space H[sup(1,p)] -- 5.4. Dirichlet regularity problem, Sobolev H[sup(1,p)] (1 &lt -- p &lt -- ∞) data -- 5.5. Dirichlet regularity problem, H[sup(1,p)] (( n…1) / n &lt -- p ≤ 1) data -- Chapter 6. The equivalence of Hardy space definitions -- 6.1. Preliminaries -- 6.2. C-suharmonicity -- 6.3. The main step -- 6.4. The equivalence theorem on C[sup(1)] domains -- 6.5. The equivalence theorem on Lipschitz domains -- Appendix A. Variable Coefficient Cauchy Integrals -- Appendix B. One Result on the Maximal Operator -- Bibliography.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.