On Gurov-Reshetnyak Property

Research output: Contribution to conferencePresentation

Abstract

In the mid of 70s, L.G.Gurov and Yu.G.Reshetnyak introduced in analogy with the definition of BMO the class which consists of all non-negative integrable on cube functions whose integral oscillations does not exceed small constant times integral means over all subcubes of the domain. This class has found interesting applications in quasi-conformal mappings and PDE's. In a joint work with A.A. Korenovskiy and A.K. Lerner we established an equivalence between the Gurov-Reshetnyak and Muckehoupt's A-infinity conditions for arbitrary absolutely continuous measures. Also, we studied maximal Gurov-Reshetnyak condition and proved that for a large class of measures satisfying Busemann-Feller type condition, it will be self-improving as the usual Gurov-Reshetnyak condition. This answers to a question raised by T.Iwaniec and V.I.Kolyada.
Original languageAmerican English
StatePublished - Oct 10 2005
EventNorthwestern University Anaylsis and Probability Seminar - Evanston, IL
Duration: Oct 10 2005 → …

Conference

ConferenceNorthwestern University Anaylsis and Probability Seminar
Period10/10/05 → …

Keywords

  • Gurov-Reshetnyak

DC Disciplines

  • Mathematics

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