Abstract Measure Grand Lebesgue Spaces and Applications

Wei Wang; Jiang Zhou

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arXiv · 2607.04201

Abstract Measure Grand Lebesgue Spaces and Applications

Wei Wang·Jiang Zhou

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Abstract

We introduce abstract measure grand Lebesgue spaces endowed with ball basis structures and investigate their fundamental properties, together with the behavior of $\mathfrak{BO}$ operators. By exploiting sparse domination for $\mathfrak{BO}$ operators and norm inequalities for sparse operators, we derive norm estimates for this class of operators. As applications, we establish that $\mathfrak{BO}$ operators encompass the maximal operators, Calder\'on-Zygmund operators on homogeneous spaces and Carleson operators.

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Wei Wang, Jiang Zhou. 2026-07-05. Abstract Measure Grand Lebesgue Spaces and Applications. https://arxiv.org/abs/2607.04201

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