iv CONTENT S Chapter 11 . Th e Proo f o f Nonhomogeneou s Cotlar' s Lemma . Arbitrar y Measure 8 3 Chapter 12 . Startin g the Proof of Nonhomogeneous Nonaccretive Tb Theorem 9 3 12.1. Termina l an d transi t cube s 9 4 12.2. Projection s A and AQ 9 6 Chapter 13 . Nex t Ste p i n Theore m 10.6 . Goo d an d Ba d Function s 10 1 13.1. Goo d function s an d ba d function s agai n 10 1 13.2. Reductio n t o estimate s o n goo d function s 10 2 13.3. Splittin g (T(p goo d,ipgood) to thre e sum s 10 3 13.4. Thre e type s o f estimates o f f fc(x, y)f{x)g{y) d/j,(x) dfj,(y) 10 4 13.5. Estimat e o f long range interactio n su m oi 10 6 13.6. Shor t rang e interactio n su m 0-3 . Nonhomogeneous paraproduct s 10 9 Chapter 14 . Estimat e o f the Diagona l Sum . Remainde r i n Theore m 3. 3 12 1 14.1. Estimat e o f S i e r m 12 3 14.2. Estimat e o f E £r 12 6 Chapter 15 . Tw o Weigh t Estimat e fo r th e Hilber t Transform . Preliminarie s 12 7 Chapter 16 . Necessit y i n th e Mai n Theore m 13 3 Chapter 17 . Tw o Weigh t Hilber t Transform . Toward s th e Mai n Theore m 13 5 17.1. Ba d an d goo d part s o f / an d g 13 6 17.2. Estimate s o n goo d function s 13 7 Chapter 18 . Lon g Rang e Interactio n 13 9 Chapter 19 . Th e Res t o f the Lon g Rang e Interactio n 14 3 Chapter 20 . Th e Shor t Rang e Interactio n 14 5 20.1. Th e estimat e o f neighbor-terms 14 5 20.2. Th e estimat e o f stopping term s 14 5 20.3. Th e choic e of stoppin g interval s 14 7 Chapter 21 . Difficul t Term s an d Severa l Paraproduct s 15 3 21.1. Firs t paraproduc t 15 4 21.2. Tw o mor e paraproduct s 15 6 21.3. Secon d paraproduct : miraculou s improvemen t o f th e Carleso n property 15 9 Chapter 22 . Two-Weigh t Hilber t Transfor m an d Maxima l Operato r 16 1 22.1. Doublin g 16 1 22.2. N o doubling 16 3 Bibliography 165
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