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Abstract. In this paper the author gives a maximal function
characterization of the Morrey-type Besov and Triebel-Lizorkin
spaces, $MB^{s,\beta}_{p,q}(\Mathbb R^n)$ and $MF^{s,\beta}_{p,q}(\Mathbb R^n)$, which
are the generalizations of the well-known Morrey-type spaces and
the inhomogeneous Besov and
Triebel-Lizorkin spaces.
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