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A characterization of some weighted norm inequalities for the fractional maximal function. (English) Zbl 0809.42009
Summary: A new characterization is given for the pairs of weight functions $$v$$, $$w$$ for which the fractional maximal function is a bounded operator from $$L^ p_ v(X)$$ to $$L^ q_ w(X)$$ when $$1< p< q<\infty$$ and $$X$$ is a homogeneous space with a group structure. The case when $$X$$ is the $$n$$- dimensional Euclidean space is included.

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory
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