变指标Fofana空间及其预对偶空间

Variable Fofana’s Spaces and Their Pre-Dual

通过引入变指标Fofana空间(Lp(·),Lq)α(Rn)(1<p(·)<∞,1≤q,α≤∞)及其预对偶空间,研究了其空间的相关性质.与此同时,利用函数分层分解和实变技巧得到了分数次积分算子及其交换子在变指标Fofana空间上有界的充分必要条件.

By introducing variable Fofana’s spaces(Lp(·),Lq)α(Rn)(1<p(·)<∞,1≤q,α≤∞)and their pre-dual spaces,we discussed the properties of those spaces.Meanwhile,via applying hierarchical decomposition of function and real variable techniques,the necessary and sufficient conditions for boundedness of fractional integral operators and their commutators on variable Fofana’s spaces are obtained.