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September 10, 2025Open Access

Hardy operators and commutators on generalized central function spaces

Key Points

The study identifies the predual of the generalized central Campanato space as the generalized central Hardy space.
Findings indicate boundedness for Hardy type operators on generalized central function spaces, providing essential characterizations.
By exploring duality, the boundedness characterization of functions in Campanato spaces enhances understanding of operator behavior.
Investigations into commutators contribute to broader applications within generalized central function spaces.

Abstract

In this article, we study the boundedness of operators of Hardy type on generalized central function spaces, such as the generalized central Hardy space \ (HA^p, r_ (Rⁿ) \), the generalized central Morrey space \ (Ṁ^p, r_ (Rⁿ) \), and the generalized central Campanato space \ (CMȮ^p, r_ (Rⁿ) \), with \ (p (1, ) \), and \ ( (t): (0, ) (0, ) \). We first show that \ (HA^p', r'_ (Rⁿ) \) is the predual of \ (CMȮ^p, r_ (Rⁿ) \). After that, we investigate the boundedness of operators of Hardy type on those spaces. By duality, we obtain the boundedness characterization of function \ (b CMȮ^p, r_ (Rⁿ) \) via the \ (Ṁ^p, r_ (Rⁿ) \) -boundedness of commutator \ (b, H^*\). For more information see https: //ejde. math. txstate. edu/Volumes/2025/82/abstr. html

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