A note on the maximal Gurov-Reshetnyak condition

A. A. Korenovskyy, A. K. Lerner, A. M. Stokolos

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In a recent paper [17] we established an equivalence between the Gurov-Reshetnyak and A conditions for arbitrary absolutely continuous measures. In the present paper we study a weaker condition called the maximal Gurov-Reshetnyak condition. Although this condition is not equivalent to A even for Lebesgue measure, we show that for a large class of measures satisfying Busemann-Feller type condition it will be self-improving as is the usual Gurov-Reshetnyak condition. This answers a question raised independently by Iwaniec and Kolyada.

Original languageEnglish
Pages (from-to)461-470
Number of pages10
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Issue number1
StatePublished - 2014


  • Maximal Gurov-Reshetnyak condition
  • Non-doubling measures
  • Self-improving properties


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