The measures with an associated square function operator bounded in $L^2$

Benjamin Jaye; Fedor Nazarov; Xavier Tolsa

The measures with an associated square function operator bounded in $L^2$

Classical Analysis and ODEs 2016-12-15 v1 Functional Analysis Metric Geometry

Authors: Benjamin Jaye , Fedor Nazarov , Xavier Tolsa

Abstract

In this paper we provide an extension of a theorem of David and Semmes ('91) to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in $L^2(\mu)$ . The description is given in terms of a modification of Jones' $\beta$ -coefficients.

Keywords

operator theory measure theory operator theory and elliptic operators

Cite

@article{arxiv.1612.04754,
  title  = {The measures with an associated square function operator bounded in $L^2$},
  author = {Benjamin Jaye and Fedor Nazarov and Xavier Tolsa},
  journal= {arXiv preprint arXiv:1612.04754},
  year   = {2016}
}

Comments

51 pages. Some basic definitions are imported from the submissions arXiv:1604.02014 and arXiv:1602.02821 with only minor changes

The measures with an associated square function operator bounded in $L^2$

Abstract

Keywords

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