Absolute continuity and α-Numbers on the real line

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dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor.author Orponen, Tuomas
dc.date.accessioned 2019-11-18T18:04:01Z
dc.date.available 2019-11-18T18:04:01Z
dc.date.issued 2019
dc.identifier.citation Orponen , T 2019 , ' Absolute continuity and α-Numbers on the real line ' , Analysis & PDE , vol. 12 , no. 4 , pp. 969-996 . https://doi.org/10.2140/apde.2019.12.969 en
dc.identifier.issn 1948-206X
dc.identifier.other PURE: 118045322
dc.identifier.other PURE UUID: b9efdfb7-142a-4a4c-be62-287bf2fa3aaf
dc.identifier.other WOS: 000448434900003
dc.identifier.other Scopus: 85057971531
dc.identifier.uri http://hdl.handle.net/10138/307023
dc.description.abstract Let mu be Radon measures on R, with mu nonatomic and nu doubling, and write mu = mu(a) + mu(s) for the Lebesgue decomposition of mu relative to nu. For an interval I subset of R, define alpha(mu,nu) (I) := W-1 (mu(I), nu(I)), the Wasserstein distance of normalised blow-ups of mu and nu restricted to I. Let S nu be the square function S-nu(2) (mu) = Sigma alpha(2)(mu,nu)(I) chi(1), where D is the family of dyadic intervals of side-length at most 1. I prove that S-nu(mu) is finite mu(a) almost everywhere and infinite mu(s) almost everywhere. I also prove a version of the result for a nondyadic variant of the square function S-nu(mu). The results answer the simplest "n = d = 1" case of a problem of J. Azzam, G. David and T. Toro. en
dc.format.extent 28
dc.language.iso eng
dc.relation.ispartof Analysis & PDE
dc.rights en
dc.subject Wasserstein distance en
dc.subject alpha-numbers en
dc.subject doubling measures en
dc.subject RECTIFIABILITY en
dc.subject OPERATORS en
dc.subject WEIGHTS en
dc.subject 111 Mathematics en
dc.title Absolute continuity and α-Numbers on the real line en
dc.type Article
dc.description.version Peer reviewed
dc.identifier.doi https://doi.org/10.2140/apde.2019.12.969
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/acceptedVersion

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