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 11
3.1. Localizatio n lemma s 11
3.2. A building bloc k fo r th e constructio n o f special measure s 13
3.3. Localizatio n o n specia l cube s 13
3.4. Modificatio n o f distribution S. Constructio n o f auxiliary measure s 14
3.5. Ahlfor s ball s 15
3.6. Th e principa l estimat e fo r auxiliar y measure s 16
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
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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