1 Introduction ................................................. 5
2 Real analysis on spaces of homogeneous type .................. 8
2.1 Spaces of homogeneous type and RD-spaces ................ 8
2.2 Dyadic cubes, covering lemmas, and the Calderón-
Zygmund decomposition .................................. 10
2.3 Space of test functions ................................ 14
2.4 Approximations of the identity ......................... 15
2.5 Singular integrals on spaces of homogeneous type ....... 17
3 Multilinear Calderón-Zygmund theory ......................... 20
3.1 Multilinear Calderón-Zygmund operators ................. 20
3.2 Multilinear weak-type estimates ........................ 21
4 Weighted multilinear Calderón-Zygmund theory ................ 26
4.1 Multiple weights ....................................... 26
4.2 Weighted estimates for the multi-sublinear maximal
function ............................................... 28
4.3 Weighted estimates for multilinear Calderón-Zygmund
operators .............................................. 34
4.4 Weighted estimates for maximal multilinear singular
integrals .............................................. 41
5 A multilinear T1-theorem on Lebesgue spaces ................. 45
5.1 Some lemmas on multilinear Calderón-Zygmund operators .. 45
5.2 BMO-boundedness of multilinear singular integrals ...... 48
5.3 A multilinear T1-theorem ............................... 49
6 Bilinear T1-theorems on Triebel-Lizorkin and Besov spaces ... 51
6.1 Bilinear weak boundedness property ..................... 51
6.2 Bilinear molecules ..................................... 57
6.3 Bilinear T1-theorem on Triebel-Lizorkin spaces ......... 64
6.4 Bilinear T1-theorem on Besov spaces .................... 75
7 Multilinear vector-valued T1 type theorems .................. 84
7.1 A multilinear off-diagonal estimate .................... 84
7.2 Quadratic T1 type theorems on Lebesgue spaces .......... 91
7.3 Quadratic T1 type theorems on Besov and Triebel-
Lizorkin spaces ........................................ 96
8 Paraproducts as bilinear Calderón-Zygmund operators ........ 101
8.1 Paraproducts .......................................... 101
8.2 Almost diagonal estimates ............................. 102
8.3 Paraproducts as bilinear Calderón-Zygmund operators ... 105
8.4 Boundedness of paraproducts on Triebel-Lizorkin and
Besov spaces .......................................... 110
9 Bilinear multiplier operators on Triebel-Lizorkin
and Besov spaces ........................................... 112
9.1 Bilinear multiplier operators ......................... 112
9.2 Off-diagonal estimates for bilinear multiplier
operators ............................................. 113
9.3 Boundedness of bilinear multiplier operators .......... 115
References .................................................... 117
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