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October 5, 2025Open Access

Characterization for Campanato norm via quasi-Banach function spaces not assuming the Fatou property

Key Points

Characterizations of Campanato norms through quasi-Banach function spaces show new mathematical frameworks.
The study advances understanding of BMO and Campanato norms using the L^p-average in broader context.
This work expands on previous findings by applying principles to function spaces without the Fatou property.
Utilizing quasi-Banach spaces allows for enhanced characterizations, pointing to new potential applications in analysis.

Abstract

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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Cite This Study

Naoya Hatano (Thu,) studied this question.

synapsesocial.com/papers/68e25385d6d66a53c2474cb1 https://doi.org/https://doi.org/10.48550/arxiv.2510.01653

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