Characterizations of the BMO and Lipschitz Spaces via Commutators on Weak Lebesgue and Morrey Spaces

被引：1
|
作者：
Wang, Ding-huai [1 ]
Zhou, Jiang [2 ]
机构：
[1] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China
[2] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2023年 / 39卷 / 03期
基金：
中国国家自然科学基金;
关键词：
BMO space; characterization; commutator; Lipschitz space; Morrey space;
D O I：
10.1007/s10255-023-1077-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the weak Morrey space WMqP is contained in the Morrey space M-q1(P) for 1 = (q1) < q = p < 8. As applications, we show that if the commutator [b, T] is bounded from L-P to L-P,L-8 for some p ? (1, 8), then b E BMO, where T is a Calder'on-Zygmund operator. Also, for 1 < p < q = 8, b ? BMO if and only if [b, T] is bounded from M-P(q) to WMPq. For b belonging to Lipschitz class, we obtain similar results.
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页码：583 / 590
页数：8
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