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Calderón-Zygmund Capacities and Operators on Nonhomogeneous Spaces
About this Title
Alexander Volberg, Michigan State University, East Lansing, MI
Publication: CBMS Regional Conference Series in Mathematics
Publication Year:
2003; Volume 100
ISBNs: 978-0-8218-3252-3 (print); 978-1-4704-2461-9 (online)
DOI: https://doi.org/10.1090/cbms/100
MathSciNet review: MR2019058
MSC: Primary 42B20; Secondary 31A15, 31C05, 32A55, 47G10
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction
- Chapter 2. Preliminaries on capacities
- Chapter 3. Localization of Newton and Riesz potentials
- Chapter 4. From distribution to measure. Carleson property
- Chapter 5. Potential neighborhood that has properties (3.13)–(3.14)
- Chapter 6. The tree of the proof
- Chapter 7. The first reduction to nonhomogeneous $Tb$ theorem
- Chapter 8. The second reduction
- Chapter 9. The third reduction
- Chapter 10. The fourth reduction
- Chapter 11. The proof of nonhomogeneous Cotlar’s lemma. Arbitrary measure
- Chapter 12. Starting the proof of nonhomogeneous nonaccretive $Tb$ theorem
- Chapter 13. Next step in theorem 10.6. Good and bad functions
- Chapter 14. Estimate of the diagonal sum. Remainder in theorem 3.3
- Chapter 15. Two-weight estimate for the Hilbert transform. Preliminaries
- Chapter 16. Necessity in the main theorem
- Chapter 17. Two-weight Hilbert transform. Towards the main theorem
- Chapter 18. Long range interaction
- Chapter 19. The rest of the long range interaction
- Chapter 20. The short range interaction
- Chapter 21. Difficult terms and several paraproducts
- Chapter 22. Two-weight Hilbert transform and maximal operator