Annales Academię Scientiarum Fennicę
Mathematica
Volumen 32, 2007, 461-470
Odessa National University, IMEM, Department of Mathematical
Analysis
Dvoryanskaya, 2, 65026 Odessa, Ukraine; anakor 'at' paco.net
Bar-Ilan University, Department of Mathematics
52900 Ramat Gan, Israel; aklerner 'at' netvision.net.il
DePaul University, Department of Mathematical Sciences
Chicago, IL, 60614, U.S.A.; astokolo 'at' depaul.edu
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.
2000 Mathematics Subject Classification: Primary 42B25.
Key words: Maximal Gurov-Reshetnyak condition, self-improving properties, non-doubling measures.
Reference to this article: A.A. Korenovskyy, A.K. Lerner and A.M. Stokolos: A note on the maximal Gurov-Reshetnyak condition. Ann. Acad. Sci. Fenn. Math. 32 (2007), 461-470.
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