Square Functions of Fractional Homogeneity and Wolff Potentials

Vasilis Chousionis, Laura Prat, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2015 The Author(s) 2015. Published by Oxford University Press. All rights reserved. In this paper it is shown that, for any measure μ in d and for a non-integer 0<s <d, the Wolff energy //∞ 0 ( μ(B(x,r)) rs )2 dr r dμ(x) is comparable to \\∞ 0 // μ(B(x, r)) rs ? μ(B(x, 2r)) (2r)s /2 dr r dμ(x), unlike in the case when s is an integer. We also study the relation with the L2-norm of s-Riesz transforms, 0>s >1, and we provide a counterexample in the integer case.
Original languageEnglish
Pages (from-to)2295-2319
JournalInternational Mathematics Research Notices
Volume2016
Issue number8
DOIs
Publication statusPublished - 1 Jan 2016

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