Parametric Marcinkiewicz integral on grand variable Herz-Morrey spaces

Liwei Wang; Xiaoyan Li; Liwei Wang; Xiaoyan Li

doi:10.3934/math.20251051

AIMS Mathematics

2025, Volume 10, Issue 10: 23652-23675. doi: 10.3934/math.20251051

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Research article

Parametric Marcinkiewicz integral on grand variable Herz-Morrey spaces

Liwei Wang ^,,
Xiaoyan Li

School of Mathematics-Physics and finance, Anhui Polytechnic University, Wuhu 241000, China

Received: 09 May 2025 Revised: 21 September 2025 Accepted: 04 October 2025 Published: 17 October 2025
MSC : 42B20, 42B35

We establish the boundedness of the parametric Marcinkiewicz integral $ \mu^\rho_\Omega $ and its higher-order commutators $ [\Lambda^m, \mu^\rho_\Omega] $ with $ \rm{BMO} $ symbols on grand variable Herz-Morrey spaces $ M\dot{K}_{\lambda, \beta(\cdot)}^{\alpha(\cdot), \gamma), \theta}({\Bbb{ R}}^n) $. These results also apply to grand variable Herz spaces, including the case where $ \alpha(\cdot) $ is constant.
- parametric Marcinkiewicz integral,
- higher-order commutator,
- grand Herz-Morrey space,
- variable exponent
Citation: Liwei Wang, Xiaoyan Li. Parametric Marcinkiewicz integral on grand variable Herz-Morrey spaces[J]. AIMS Mathematics, 2025, 10(10): 23652-23675. doi: 10.3934/math.20251051

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Abstract

We establish the boundedness of the parametric Marcinkiewicz integral $ \mu^\rho_\Omega $ and its higher-order commutators $ [\Lambda^m, \mu^\rho_\Omega] $ with $ \rm{BMO} $ symbols on grand variable Herz-Morrey spaces $ M\dot{K}_{\lambda, \beta(\cdot)}^{\alpha(\cdot), \gamma), \theta}({\Bbb{ R}}^n) $. These results also apply to grand variable Herz spaces, including the case where $ \alpha(\cdot) $ is constant.

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