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This research explores Campanato norms through quasi-Banach function spaces without the Fatou property, indicating broader frameworks.
It is well known that the BMO and Campanato norms can be characterized using the Lᵖ-average. These characterizations were later generalized to averages taken over various types of function spaces. In particular, generalizations using Banach function spaces were provided by Ho, Izuki, Noi, and Sawano. In this paper, as a further generalization, we provide similar characterizations using quasi-Banach function spaces that do not assume the Fatou property.
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Naoya Hatano (2025) studied this question.
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