Integrable fractional mean functions on spaces of homogeneous type

Details Integrable fractional mean functions on spaces of homogeneous type Integrable fractional mean functions on spaces of homogeneous type

2009-01-16

arxiv.org/abs/0901.2524v4

African Diaspora Journal of Mathematics, Volume 9, Number 1, pp. 8-30 (2010)

Mathematics

Classical Analysis and ODEs

23 pages, we have change the title and correct some typing errors

Scientific paper

The class of Banach spaces $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$, $1\leq q\leq \alpha \leq p\leq \infty ,$ introduced in \cite{F1} in connection with the study of the continuity of the fractional maximal operator of Hardy-Littlewood and of the Fourier transformation in the case $% X=\mathbb{R}^{n}$ and $\mu $ is the Lebesgue measure, was generalized in \cite{FFK} to the setting of homogeneous groups. We generalize it here to spaces of homogeneous type and we prove that the results obtained in \cite{FFK} such as relations between these spaces and Lebesgue spaces, weak Lebesgue and Morrey spaces, remain true.

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