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arXiv · 0901.2524

Integrable fractional mean functions on spaces of homogeneous type

Justin Feuto·Ibrahim Fofana·Konin Koua
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Abstract

The class of Banach spaces $(L^{q},L^{p}) ^α(X,d,μ)$, $1\leq q\leq α\leq p\leq \infty ,$ 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 $μ$ 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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Justin Feuto, Ibrahim Fofana, Konin Koua. 2009-05-31. Integrable fractional mean functions on spaces of homogeneous type. https://arxiv.org/abs/0901.2524

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