Integrable fractional mean functions on spaces of homogeneous type

Abstract

The class of Banach spaces $(L^q,L^p{)}^{\alpha }(X,d,\mu )$, $1\le q\le \alpha \le p\le \infty ,$ 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 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.

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

References in corpus (1)

• Espaces de fonctions à moyenne fractionnaire intégrable sur les groupes localement compacts