Abstract:This paper extends the self-improvement result of Keith and Zhong in [16] to the two-measure case. Our main result shows that a two-measure (p, p)-Poincaré inequality for 1 < p < ∞ improves to a (p, p − ε)-Poincaré inequality for some ε > 0 under a balance condition on the measures. The corresponding result for a maximal Poincaré inequality is also considered. In this case the left-hand side in the Poincaré inequality is replaced with an integral of a sharp maximal function and the results hold without a bala… Show more
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