An extension of the characterization of CMO and its application to compact commutators on Morrey spaces
An extension of the characterization of CMO and its application to compact commutators on Morrey spaces
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发表时间：
2019
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通讯作者：
Ryutaro;Eiichi
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作者：
Ryutaro;Eiichi
1978年内山给出了CMO（Rn）的特征证明，CMO（Rn）是C∞ comp（R）在BMO（Rn）中的闭包。我们将这一刻画推广到了具有可变增长条件的Campanato空间中C∞ comp（R）的闭包.作为应用，我们刻画了具有可变增长条件的Morrey空间上的紧算子[B，T ]和[B，Iα]，其中T是Calderón-Zygmund奇异积分算子，Iα是分数次积分算子，B是具有可变增长条件的Campanato空间中的函数.
In 1978 Uchiyama gave a proof of the characterization of CMO(Rn) which is the closure of C∞ comp(R) in BMO(Rn). We extend the characterization to the closure of C∞ comp(R) in the Campanato space with variable growth condition. As an application we characterize compact commutators [b, T ] and [b, Iα] on Morrey spaces with variable growth condition, where T is the Calderón-Zygmund singular integral operator, Iα is the fractional integral operator and b is a function in the Campanato space with variable growth condition.