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Criteria of strong type two-weighted inequalities for fractional maximal functions. (English) Zbl 0884.42015
The main result of this paper is a characterization of the boundedness of a fractional maximal operator from a weighted Lebesgue space L p (w) into L q (w) on a homogeneous type space X, 1<p<q<. The key ingredients of proof are earlier results of the authors and a generalization of the classical result of E. T. Sawyer [Stud. Math. 75, 1-11 (1982; Zbl 0508.42023)] to the context of homogeneous type spaces.
Reviewer: L.Pick (Praha)

42B25Maximal functions, Littlewood-Paley theory
42B20Singular and oscillatory integrals, several variables