可变Fofana空间及其预对偶
Variable Fofana's Spaces and their Pre-dual
摘要：
本文引入了变量Fofana空间$(L^{p(\cdot)},L^q)^α(\mathbb{R}^n)$，其中$1< p(\cdot)<\infty$和$1\leq q,α\leq\infty$，给出了这类空间的一些性质，并建立了这类空间的预对偶，这有助于证明分数次积分算子有界的必要条件.作为应用，讨论了变量Fofana空间上的分数次积分算子和分数次积分算子的特征，这些结果对于经典的Fofana空间也是新的结果.
英文摘要：
In this paper, we introduce the variable Fofana's spaces $(L^{p(\cdot)},L^q)^α(\mathbb{R}^n)$ where $1< p(\cdot)<\infty$ and $1\leq q,α\leq\infty$, then show some properties and establish the pre-dual of those spaces which are contributed to prove the necessary conditions of fractional integral commutators' boundedness. As applications, the characterization of fractional integral operators and commutators on variable Fofana's spaces are discussed, which are new result even for the classical Fofana's spaces.
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