Capacities associated with scalar signed riesz kernels, and analytic capacity

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Analytic capacity is associated with the Cauchy kernel 1/z and the space L∞. One has likewise capacities associated with the real and imaginary parts of the Cauchy kernel and L∞. Striking results of Tolsa and a simple remark show that these three capacities are comparable. We present an extension of this fact to Rn, n ≥ 3, involving the vector-valued Riesz kernel of homogeneity -1 and n - 1 of its components.
Original languageEnglish
Pages (from-to)1319-1361
JournalIndiana University Mathematics Journal
Volume60
Issue number4
DOIs
Publication statusPublished - 1 Dec 2011

Keywords

  • Analytic capacity
  • Linear growth. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 42B20
  • Scalar signed Riesz kernels

Fingerprint Dive into the research topics of 'Capacities associated with scalar signed riesz kernels, and analytic capacity'. Together they form a unique fingerprint.

Cite this