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Preface; 1 Potential Theory and Weighted Norm Inequalities for Singular Integrals; 1.1 Singular Integrals and Weighted Inequalities; 2 Degenerate Elliptic Equations, Subelliptic Operators, and Monge-Ampére Equations; 2.1 Two Weight Norm Inequalities for Fractional Integrals; 2.2 Fefferman-Phong and Hörmander Regularity; 2.3 The Monge-Ampére Equation; 3 Papers by Richard Wheeden Referred to in the Preface; References; 4 Other Papers Referred to in the Preface; References; Contents; On Some Pointwise Inequalities Involving Nonlocal Operators; 1 Introduction; 2 Some New Inequalities
2.1 A Pointwise Inequality for Nonlocal Operators in Non-divergence Form2.2 The Case of Translation Invariant Kernels; 2.3 Some Integral Operators on Geometric Spaces; 2.3.1 The Case of Lie Groups; 2.3.2 The Case of Manifolds; 3 A Review of the Extension Property; 3.1 The Extension Property in Rn; 3.2 The Extension Property in Bounded Domains; 3.3 The Extension Property in General Frameworks; 4 Proofs of Theorems 1.1 and 1.2; 4.1 Proof of Theorem 1.1; 4.2 Proof of Theorem 1.2; 4.3 The Results in Bounded Domains; 5 Geometric Ambient Spaces; 5.1 The Case of Manifolds; 5.2 The Case of Lie Groups
Form-Invariance of Maxwell Equations in Integral Form1 Introduction; 2 Maxwell Equations; 2.1 Maxwell Equations in Integral Form; 3 Changes of Coordinates; 4 Invariance Properties of (5)-(8); 4.1 Invariance of (5) and (6) by Changes of Coordinates; 4.2 Invariance of (7) and (8) by Changes of Coordinates; 4.3 Conclusion; References; Chern-Moser-Weyl Tensor and Embeddings into Hyperquadrics; 1 Introduction; 2 Chern-Moser-Weyl Tensor for a Levi Non-degenerate Hypersurface ; 3 Transformation Law for the Chern-Moser-Weyl Tensor; 4 A Monotonicity Theorem for the Chern-Moser-Weyl Tensor
5 Counter-Examples to the Embeddability Problem for Compact Algebraic Levi Non-degenerate Hypersurfaces with Positive Signature into Hyperquadrics6 Non-embeddability of Compact Strongly Pseudo-Convex Real Algebraic Hypersurfaces into Spheres; References; The Focusing Energy-Critical Wave Equation; References; Densities with the Mean Value Property for Sub-Laplacians: An Inverse Problem; 1 Introduction; 2 Sub-Laplacians and Related Triples; 3 Results on the Inverse Problem for L; 4 Proofs of the Results on the Inverse Problem; Appendix: L-Superharmonic Functions; References
2.1 A Pointwise Inequality for Nonlocal Operators in Non-divergence Form2.2 The Case of Translation Invariant Kernels; 2.3 Some Integral Operators on Geometric Spaces; 2.3.1 The Case of Lie Groups; 2.3.2 The Case of Manifolds; 3 A Review of the Extension Property; 3.1 The Extension Property in Rn; 3.2 The Extension Property in Bounded Domains; 3.3 The Extension Property in General Frameworks; 4 Proofs of Theorems 1.1 and 1.2; 4.1 Proof of Theorem 1.1; 4.2 Proof of Theorem 1.2; 4.3 The Results in Bounded Domains; 5 Geometric Ambient Spaces; 5.1 The Case of Manifolds; 5.2 The Case of Lie Groups
Form-Invariance of Maxwell Equations in Integral Form1 Introduction; 2 Maxwell Equations; 2.1 Maxwell Equations in Integral Form; 3 Changes of Coordinates; 4 Invariance Properties of (5)-(8); 4.1 Invariance of (5) and (6) by Changes of Coordinates; 4.2 Invariance of (7) and (8) by Changes of Coordinates; 4.3 Conclusion; References; Chern-Moser-Weyl Tensor and Embeddings into Hyperquadrics; 1 Introduction; 2 Chern-Moser-Weyl Tensor for a Levi Non-degenerate Hypersurface ; 3 Transformation Law for the Chern-Moser-Weyl Tensor; 4 A Monotonicity Theorem for the Chern-Moser-Weyl Tensor
5 Counter-Examples to the Embeddability Problem for Compact Algebraic Levi Non-degenerate Hypersurfaces with Positive Signature into Hyperquadrics6 Non-embeddability of Compact Strongly Pseudo-Convex Real Algebraic Hypersurfaces into Spheres; References; The Focusing Energy-Critical Wave Equation; References; Densities with the Mean Value Property for Sub-Laplacians: An Inverse Problem; 1 Introduction; 2 Sub-Laplacians and Related Triples; 3 Results on the Inverse Problem for L; 4 Proofs of the Results on the Inverse Problem; Appendix: L-Superharmonic Functions; References