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arXiv · 2007.00468

Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

Minglei Shi·Ryutaro Arai·Eiichi Nakai
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Abstract

We consider the commutators $[b,T]$ and $[b,I_{\rho}]$ on Orlicz-Morrey spaces, where $T$ is a Calder\'on-Zygmund operator, $I_{\rho}$ is a generalized fractional integral operator and $b$ is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional maximal operators on Orlicz-Morrey spaces. Moreover, we introduce Orlicz-Campanato spaces and establish their relations to Orlicz-Morrey spaces.

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Minglei Shi, Ryutaro Arai, Eiichi Nakai. 2020-06-30. Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces. https://arxiv.org/abs/2007.00468

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