1. Introduction ................................................. 5
2. WSIO's of convolution type .................................. 13
2.1. Homogeneous Besov spaces ............................... 13
2.2. Boundedness of convolution operators ................... 17
2.3. Unbounded operators .................................... 23
3. WSIO's with global kernels .................................. 27
3.1. Reduced T1 theorem in  n ............................... 27
3.2. BMO-type spaces on domains ............................. 40
3.3. Endpoint estimates for restricted operators ............ 45
3.4. TΧΩ, theorem for restricted operators .................. 51
4. Regularity of standard kernels .............................. 62
4.1. Kernel spaces .......................................... 62
4.2. Dyadic resolution of unity ............................. 64
4.3. Regularity of kernels in uniform domains ............... 71
5. Extension of smooth kernels ................................. 79
5.1. Hölder spaces .......................................... 79
5.2. Uniformity and products ................................ 86
5.3. Atomic decomposition and kernel extension .............. 89
6. WSIO's on domains ........................................... 96
6.1. Admissible domains ..................................... 96
6.2. TΧΩ, theorem revisited ................................. 98
6.3. T1 theorem on admissible domains ....................... 99
Appendix A. Notation .......................................... 102
Appendix B. Compactly supported wavelets ...................... 105
Appendix C. Whitney decomposition ............................. 107
References .................................................... 109
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