Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
Author | : Xavier Tolsa |
Publisher | : American Mathematical Soc. |
Total Pages | : 142 |
Release | : 2017-01-18 |
ISBN-10 | : 9781470422523 |
ISBN-13 | : 1470422522 |
Rating | : 4/5 (522 Downloads) |
Download or read book Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform written by Xavier Tolsa and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the proof of two related results. The first one asserts that if is a Radon measure in satisfyingfor -a.e. , then is rectifiable. Since the converse implication is already known to hold, this yields the following characterization of rectifiable sets: a set with finite -dimensional Hausdorff measure is rectifiable if and only ifH^1x2EThe second result of the monograph deals with the relationship between the above square function in the complex plane and the Cauchy transform . Assuming that has linear growth, it is proved that is bounded in if and only iffor every square .