B_σ-grand Morrey spaces

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Abstract

In this paper, we define the B_σ-type grand Morrey spaces and establish the extrapolation theorem on the B_σ-type grand Morrey spaces. In the process of proving the theorem, we find that the predual spaces of these spaces are H_σ-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_σ-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_σ type grand Morrey space.

Keywords

grand Lebesgue space / B_σ type space / extrapolation theory / BMO space

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