齐型空间上的可积分数平均函数
Integrable fractional mean functions on spaces of homogeneous type
摘要：
巴拿赫空间类$(L^{q},L^{p}) ^α(X,d,μ)$，$1\leq q\leq α\leq p\leq \infty ,$在\cite{F1}中引入，与研究Hardy-Littlewood的分数极大算子的连续性和在$% X=\mathbb{R}^{n}$和$μ$是勒贝格测度的情况下的傅里叶变换有关，在\cite{FFK}中推广到齐次群的设置。我们在这里推广到空间的齐型，我们证明了在\cite{FFK}，如这些空间和Lebesgue空间，弱Lebesgue和Morrey空间之间的关系，得到的结果仍然正确。
英文摘要：
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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