一类新型BMO空间

Some New Classes of BMO Spaces

引进了弱型有界平均震荡函数空间WBMO_q,1<q<∞,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.

We introduce the weak bounded mean oscillation spaces WBMOq, 1 〈 q 〈 ∞, which are the analog of weak Lebesgue spaces Lq,∞ in the setting of BMO space. It is obtained that the equivalence between the norms ｜｜·｜｜＊ （the BMO norm） and ｜｜·｜｜ HWBMOq. As an application, we show that the commutator [b, In] is bounded from Lp to Lq,∞for some p E （1, oo） and 1/q = 1/p - a/n, if and only if b E BMO, where In is a fractional integral operator. Also, we introduce and study the weak central bounded mean oscillation spaces Wq.