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Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type. (English) Zbl 0846.42013

Authors’ abstract: “ We give a characterization of the pairs of weights \((v, w)\), with \(w\) in the class \(A_\infty\) of Muckenhoupt, for which the fractional maximal function is a bounded operator from \(L^p (X, v d\mu)\) to \(L^q (X, w d\mu)\) when \(1< p\leq q< \infty\) and \(X\) is a space of homogeneous type.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
43A85 Harmonic analysis on homogeneous spaces
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