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Integrable Fractional Mean Functions on Spaces of Homogeneous Type

Volume 9, Number 1 (2010), 8 - 30

Integrable Fractional Mean Functions on Spaces of Homogeneous Type

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Abstract

The class of Banach spaces (Lq;Lp)a (X;d;μ), 1 · q · a · p · ¥; introduced in [10] in connection with the study of the continuity of the fractional maximal operator of Hardy-Littlewood and of the Fourier transformation in the case X = Rn and μ is the Lebesgue measure, was generalized in [7] to the setting of homogeneous groups. We generalize it here to spaces of homogeneous type and we prove that the results obtained in [7] such as relations between these spaces and Lebesgue spaces, weak Lebesgue and Morrey spaces, remain true.