A Note on the Maximal Gurov-Reshetnyak Condition

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

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Abstract

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 languageAmerican English
JournalAnnales Academiæ Scientiarum Fennicæ
Volume32
StatePublished - 2007

Keywords

  • Maximal Gurov-Reshetnyak Condition

DC Disciplines

  • Mathematics

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