Riesz transforms of non-integer homogeneity on uniformly disconnected sets

Maria Carmen Reguera, Xavier Tolsa

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
134 Downloads (Pure)

Abstract

In this paper we obtain precise estimates for the L2 norm of the s-dimensional Riesz transforms on very general measures supported on Cantor sets in Rd, with d − 1 <s<d. From these estimates we infer that, for the so-called uniformly disconnected compact sets, the capacity γs associated with the Riesz kernel x/|x| s+1 is comparable to the capacity C˙ 2 3 (d−s), 3 2 from non-linear potential theory.
Original languageEnglish
Pages (from-to)7045–7095
JournalTransactions of the American Mathematical Society
Volume368
Issue number10
Early online date10 Feb 2016
DOIs
Publication statusPublished - Oct 2016

Keywords

  • math.CA
  • math.AP

Fingerprint

Dive into the research topics of 'Riesz transforms of non-integer homogeneity on uniformly disconnected sets'. Together they form a unique fingerprint.

Cite this