Multilinear Singular Integral Forms of Christ-Journé Type.

Cover -- Title page -- Chapter 1. Introduction -- 1.1. The -commutators -- 1.2. Background and historical remarks -- Motivation -- Previous results -- 1.3. Towards a more general result -- Selected Notation -- Chapter 2. Statements of the main results -- 2.1. The classes \sK_{\eps} -- 2.2. Decomposition of kernels in \sK_{\eps} -- 2.3. Boundedness of multilinear forms -- 2.4. Remarks on Besov spaces -- 2.4.1. Equivalent norms -- 2.4.2. The role of projective space -- Chapter 3. Kernels -- 3.1. Independence of -- 3.2. Proof of Theorem 2.6 -- 3.2.1. Proof of Proposition 3.2 -- 3.2.2. Proof of Proposition 3.3 -- Chapter 4. Adjoints -- 4.1. Proof of Theorem 2.9 -- 4.2. Proof of Propositions 4.3 and 4.4 -- 4.2.1. Preparatory Results -- 4.2.2. Proof of Proposition 4.3 -- 4.2.3. Proof of Proposition 4.4 -- 4.3. A decomposition lemma -- 4.4. Invariance properties -- 4.5. The role of projective space, revisited -- Chapter 5. Outline of the proof of boundedness -- The main estimates -- Chapter 6. Some auxiliary operators -- 6.1. Proof of Proposition 6.5 -- 6.2. A decomposition result for functions in \sU -- Chapter 7. Basic ² estimates -- 7.1. An ² estimate for rough kernels -- 7.1.1. Applying the Leibniz rule -- 7.1.2. Proof of Proposition 7.6 -- 7.1.3. Proof of Theorem 7.1 -- 7.2. Generalizations of Theorem 7.1 -- Chapter 8. Some results from Calderón-Zygmund theory -- 8.1. Classes of kernels -- 8.1.1. Schur Norms and Regularity Conditions -- 8.1.2. Singular Integral Kernels -- 8.1.3. Integral conditions for singular integrals -- 8.1.4. Kernels with cancellation -- 8.1.5. On operator topologies -- 8.1.6. Consequences for sums of dilated kernels -- 8.2. On a result of Journé -- 8.3. Sums of dilated kernels -- Chapter 9. Almost orthogonality -- Chapter 10. Boundedness of Multilinear Singular Forms -- 10.1. Proof of the main theorem: Part I.

Proof of Theorem 10.1 -- 10.2. Proof of the main theorem: Part II -- 10.2.1. The main ² estimate -- 10.2.2. Proof of Theorem 10.2 -- 10.2.3. Proof that Theorem 10.2 implies Part II of Theorem 5.1 -- 10.3. Proof of the main theorem: Part III -- 10.4. Proof of the main theorem: Part IV -- 10.4.1. Outline of the proof of Theorem 10.20 -- 10.4.2. \Op_{\eps}-bounds and the proof of Proposition 10.22 -- 10.4.3. Proof of the bound (10.50), concluded -- 10.5. Proof of the main theorem: Part V -- 10.5.1. Basic decompositions -- 10.5.2. Proof of the bound (10.73) -- Chapter 11. Interpolation -- Bibliography -- Back Cover.

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