一类新型BMO空间

引进了弱型有界平均震荡函数空间WBMO_q,1q∞,它是类似于弱型勒贝格空间L~(q,∞)所对应的BMO空间.证明了‖·‖*(BMO范数)与‖·‖_(WBMO_q)之间的等价特征刻画.作为应用,对于p∈(1,∞)和1/q=1/p-α/n,交换子b,I_α]是从Lp到L~(q,∞)的有界算子,当且仅当局部可积函数b属于BMO空间,其中I_α表示分数次积分算子.另外,还引进以及学习了弱型的中心有界平均震荡空间W_q.

Some New Classes of BMO Spaces

We introduce the weak bounded mean oscillation spaces WBMO_q, 1 < q < ∞, which are the analog of weak Lebesgue spaces L^q,∞ in the setting of BMO space. It is obtained that the equivalence between the norms||·||_* (the BMO norm) and||·||_WBMOq. As an application, we show that the commutatorb,I_α] is bounded from L^p to L^q,∞ for some p∈(1,∞) and 1/q=1/p-α/n, if and only if b∈ BMO, where I_α is a fractional integral operator. Also, we introduce and study the weak central bounded mean oscillation spaces W_q.