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

作　　者：Ding-huai WANG Jiang ZHOU 

机构地区：[1]School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China [2]College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第3期583-590,共8页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No.12101010);the Natural Science Foundation of Anhui Province (No.2108085QA19)

摘　　要：We prove that the weak Morrey space W M_(q)^(p) is contained in the Morrey space M_(q1)^(p) for 1 ≤ q1<q ≤ p < ∞. As applications, we show that if the commutator [b, T ] is bounded from L^(p) to L^(p,∞) for some p ∈(1, ∞), then b ∈ BMO, where T is a Calderón-Zygmund operator. Also, for 1 < p ≤ q < ∞, b ∈ BMO if and only if [b, T ] is bounded from M_(q)^(p) to WM_(q)^(p). For b belonging to Lipschitz class, we obtain similar results.

关 键 词：BMO space characterization COMMUTATOR Lipschitz space Morrey space 

分 类 号：O177[理学—数学]