Abstract
In a recent paper [17] we established an equivalence between the Gurov-Reshetnyak and A\infty 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\infty 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 language | American English |
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Pages (from-to) | 461-470 |
Journal | Annales Academiae Scientiarum Fennicae. Mathematica |
Volume | 32 |
State | Published - 2007 |