An extension of the characterization of $\mathrm{CMO}$ and its application to compact commutators on Morrey spaces

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  • An extension of the characterization of CMO and its application to compact commutators on Morrey spaces

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<p>In 1978 Uchiyama gave a proof of the characterization of CMO(ℝ𝑛) which is the closure of 𝐶∞comp(ℝ𝑛) in BMO(ℝ𝑛). We extend the characterization to the closure of 𝐶∞comp(ℝ𝑛) 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.</p>

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