Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
American Mathematical Society (Verlag)
978-1-4704-2252-3 (ISBN)
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Xavier Tolsa, ICREA, Barcelona, Spain, and Universitat Autonoma de Barcelona, Spain.
Introduction
Preliminaries
A compactness argument
The dyadic lattice of cells with small boundaries
The Main Lemma
The stopping cells for the proof of Main Lemma 5.1
The measure $/tilde/mu$ and some estimates about its flatness}
The measure of the cells from $/mathsf{BCF}$, $/mathsf{LD}$, $/mathsf{BSD}$ and $/mathsf{BCG}$
The new families of cells $/mathsf{BS}/beta$, $/mathsf{NTerm}$, $/mathsf{NGood}$, $/mathsf{NQgood}$ and $/mathsf{NReg}$
The approximating curves $/Gamma^k$
The small measure $/tilde/mu$ of the cells from $/mathsf{BS}/beta$
The approximating measure $/nu^k$ on $/Gamma^k_{ex}$
Square function estimates for $/nu^k$
The good measure $/sigma^k$ on $/Gamma^k$
The $L^2(/sigma^k)$ norm of the density of $/nu^k$ with respect to $/sigma^k$
The end of the proof of the Main Lemma 5.1
Proof of Theorem 1.3: Boundedness of $T_/mu$ implies boundedness of the Cauchy transform
Some Calderon-Zygmund theory for $T_/mu$
Proof of Theorem 1.3: Boundedness of the Cauchy transform implies boundedness of $T_/mu$
Bibliography.
| Erscheinungsdatum | 31.01.2017 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 215 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-2252-2 / 1470422522 |
| ISBN-13 | 978-1-4704-2252-3 / 9781470422523 |
| Zustand | Neuware |
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