In a recent paper  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.
|Number of pages||10|
|Journal||Annales Academiae Scientiarum Fennicae Mathematica|
|State||Published - 2014|
- Maximal Gurov-Reshetnyak condition
- Non-doubling measures
- Self-improving properties