iv CONTENTS Chapter 6. Preliminary Results of Analysis 55 6.1. Preliminary Inequalities 55 6.2. Basic Lp estimates 56 Chapter 7. Proof of Sufficiency 59 7.1. Statement of Sufficiency Theorem 59 7.2. Main Estimate for Low Rank Case 60 7.3. Proof of Theorem 7.1 62 Chapter 8. Necessity Theorem 71 8.1. Transitivity Rule for Dual Faces 71 8.2. Lemma for Necessity 75 8.3. Necessity Theorem 77 Chapter 9. Preliminary Lemmas for Necessity Proof 81 9.1. Exclusiveness of Odd Sets 81 9.2. Scheme of Necessity Proof 89 Chapter 10. Proof of Necessity 93 10.1. Proof of Lemma 9.2 93 10.2. Proof of Lemma 9.3 97 Chapter 11. Proofs of Corollary 3.1 and Main Theorem 3.1 103 11.1. Proof of Corollary 3.1 103 11.2. Proof of Sufficient Part of Main Theorem 3.1 105 11.3. Proof of Necessity Part of Main Theorem 3.1 108 Chapter 12. Appendix 113 Bibliography 119
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