Contents Chapter 1 . Introductio n 1 Chapter 2 . Preliminarie s o n Capacitie s 7 Chapter 3 . Localizatio n o f Newton an d Ries z Potential s 1 1 3.1. Localizatio n lemma s 1 1 3.2. A building bloc k fo r th e constructio n o f special measure s 1 3 3.3. Localizatio n o n specia l cube s 1 3 3.4. Modificatio n o f distribution S. Constructio n o f auxiliary measure s 1 4 3.5. Ahlfor s ball s 1 5 3.6. Th e principa l estimat e fo r auxiliar y measure s 1 6 Chapter 4 . Fro m Distributio n t o Measure . Carleso n Propert y 2 1 Chapter 5 . Potentia l Neighborhoo d tha t ha s Propertie s (3.13)-(3.14 ) 2 5 5.1. Capacitie s wit h Calderon-Zygmun d (CZ ) kernel s 2 6 5.2. Variationa l capacit y an d extrema l measure s 3 3 5.3. L p theor y o f nonhomogeneous C Z operators. Measur e o f order m 4 2 5.4. Ries z an d Cauch y kernels : 7 + x j o p 4 5 5.5. Cauch y kerne l an d analyti c capacit y 4 7 Chapter 6 . Th e Tre e of the Proo f 5 1 Chapter 7 . Th e Firs t Reductio n t o Nonhomogeneou s Tb Theore m 5 5 Chapter 8 . Th e Secon d Reductio n 6 1 8.1. Suppresse d kernel s 6 1 8.2. Fro m real-value d kerne l t o vecto r value d kerne l 6 7 8.3. Fro m on e lattic e t o tw o lattices 6 8 8.4. Cor e suppression 6 9 Chapter 9 . Th e Thir d Reductio n 7 1 Chapter 10 . Th e Fourt h Reductio n 7 3 10.1. // , 6, D, 77 decompositio n 7 3 10.2. Goo d function s an d ba d function s 7 4 10.3. Estimate s o f nonhomogeneous Calderon-Zygmun d operator s o n goo d functions 7 6 10.4. Th e reductio n o f Theore m 9. 1 t o estimate s o f nonhomogeneou s Calderon-Zygmund operator , namel y t o Theore m 10. 6 7 8
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