A Note on the Gurov - Reshetnyak Condition
نویسنده
چکیده
An equivalence between the Gurov-Reshetnyak GR(ε) and Muckenhoupt A∞ conditions is established. Our proof is extremely simple and works for arbitrary absolutely continuous measures. Throughout the paper, μ will be a positive measure on R absolutely continuous with respect to Lebesgue measure. Denote Ωμ(f ;Q) = 1 μ(Q) ∫ Q |f(x) − fQ,μ|dμ(x), fQ,μ = 1 μ(Q) ∫
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