Riesz transforms of non-integer homogeneity on uniformly disconnected sets

Maria Carmen Reguera, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2016 American Mathematical Society. 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 ˙C⅔ (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
DOIs
Publication statusPublished - 1 Oct 2016

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