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arXiv · 1207.7118

Dyadic A1 weights and equimeasurable rearrangements of functions

Eleftherios Nikolidakis
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Abstract

We prove that the decreasing rearrangement of a dyadic A1 weight w with dyadic A1 constant [w]_{1,T}=c with respect to a tree T of homogeneity k,on a non-atomic probability space, is a usual A1 weight on (0,1] with A1 constant not more than kc-k+1.We prove also that the result is sharp, when one considers all such weights w.

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Eleftherios Nikolidakis. 2012-07-30. Dyadic A1 weights and equimeasurable rearrangements of functions. https://arxiv.org/abs/1207.7118

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