$ B_{\sigma} $-grand Morrey spaces

Yixiang Wang; Jiang Zhou; Yixiang Wang; Jiang Zhou

doi:10.3934/era.2025303

Electronic Research Archive

2025, Volume 33, Issue 11: 6865-6884. doi: 10.3934/era.2025303

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Research article

$ B_{\sigma} $-grand Morrey spaces

Yixiang Wang ,
Jiang Zhou ^,

College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China

Received: 05 July 2025 Revised: 30 October 2025 Accepted: 06 November 2025 Published: 17 November 2025

In this paper, we define the $ B_{\sigma} $-type grand Morrey spaces and establish the extrapolation theorem on the $ B_{\sigma} $-type grand Morrey spaces. In the process of proving the theorem, we find that the predual spaces of these spaces are $ H_{\sigma} $-block spaces and obtain the boundedness of the Hardy–Littlewood maximal operator on the predual spaces. By the extrapolation theory, the boundedness of the Calderón–Zygmund operator and commutators on the nonhomogeneous $ B_{\sigma} $-type grand Morrey space is also obtained. In particular, the classical bounded mean oscillation (BMO) spaces are characterized by establishing the John–Nirenberg inequality on the nonhomogeneous $ B_{\sigma} $ type grand Morrey space.
- grand Lebesgue space,
- $ B_{\sigma} $ type space,
- extrapolation theory,
- BMO space
Citation: Yixiang Wang, Jiang Zhou. $ B_{\sigma} $-grand Morrey spaces[J]. Electronic Research Archive, 2025, 33(11): 6865-6884. doi: 10.3934/era.2025303

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Abstract

In this paper, we define the $ B_{\sigma} $-type grand Morrey spaces and establish the extrapolation theorem on the $ B_{\sigma} $-type grand Morrey spaces. In the process of proving the theorem, we find that the predual spaces of these spaces are $ H_{\sigma} $-block spaces and obtain the boundedness of the Hardy–Littlewood maximal operator on the predual spaces. By the extrapolation theory, the boundedness of the Calderón–Zygmund operator and commutators on the nonhomogeneous $ B_{\sigma} $-type grand Morrey space is also obtained. In particular, the classical bounded mean oscillation (BMO) spaces are characterized by establishing the John–Nirenberg inequality on the nonhomogeneous $ B_{\sigma} $ type grand Morrey space.

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