Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform

Released on by Xavier Tolsa
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  • Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform Book Detail

  • Author : Xavier Tolsa
  • Release Date : 2017-01-18
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 142
  • ISBN 13 : 1470422522
  • File Size : 79,79 MB
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Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform by Xavier Tolsa PDF Summary

Book Description: 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 .

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