Reflectionless measures for Calderón–Zygmund operators II: Wolff potentials and rectifiability

  • Benjamin Jaye

    Clemson University, USA
  • Fedor Nazarov

    Kent State University, USA
Reflectionless measures for Calderón–Zygmund operators II: Wolff potentials and rectifiability cover

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Abstract

We continue our study of the reflectionless measures associated to an -dimensional Calderón–Zygmund operator (CZO) acting in with . Here, our focus will be the study of CZOs that are rigid, in the sense that they have few reflectionless measures associated to them. Our goal is to prove that the rigidity properties of a CZO impose strong geometric conditions upon the support of any measure  for which is a bounded operator in . In this way, we shall reduce certain well-known problems at the interface of harmonic analysis and geometric measure theory to a description of reflectionless measures of singular integral operators. What is more, we show that this approach yields promising new results.

Cite this article

Benjamin Jaye, Fedor Nazarov, Reflectionless measures for Calderón–Zygmund operators II: Wolff potentials and rectifiability. J. Eur. Math. Soc. 21 (2019), no. 2, pp. 549–583

DOI 10.4171/JEMS/844