Grand weighted variable Herz-Morrey spaces estimate for some operators

Ming Liu; Binhua Feng; Ming Liu; Binhua Feng

doi:10.3934/cam.2025012

Communications in Analysis and Mechanics

2025, Volume 17, Issue 1: 290-316. doi: 10.3934/cam.2025012

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Grand weighted variable Herz-Morrey spaces estimate for some operators

Ming Liu ^1,2,
Binhua Feng ^{1,2
,
,}

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
Shool of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China

Received: 19 July 2024 Revised: 18 November 2024 Accepted: 04 March 2025 Published: 19 March 2025
46E30, 47G10

In this paper, we established the boundedness of higher-order commutators $ I_{\beta, b}^{m} $ generated by the fractional integral operator with BMO functions on grand weighted variable-exponent Herz-Morrey spaces $ \mathrm{M\dot{K}}_{\lambda, p(\cdot)}^{\alpha, r), \theta}(\omega) $. We also obtained the boundedness of the $ m- $order multilinear fractional Hardy operator $ \mathcal{H}_{\beta, m} $ and its adjoint operator $ \mathcal{H}^{\ast}_{\beta, m} $ on weighted variable-exponent Herz-Morrey spaces $ \mathrm{M\dot{K}}_{q, p(\cdot)}^{\alpha, \lambda}(\omega) $.
- grand weighted,
- Herz-Morrey spaces,
- fractional integrals operator,
- fractional Hardy operator,
- variable exponent
Citation: Ming Liu, Binhua Feng. Grand weighted variable Herz-Morrey spaces estimate for some operators[J]. Communications in Analysis and Mechanics, 2025, 17(1): 290-316. doi: 10.3934/cam.2025012

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Abstract

In this paper, we established the boundedness of higher-order commutators $ I_{\beta, b}^{m} $ generated by the fractional integral operator with BMO functions on grand weighted variable-exponent Herz-Morrey spaces $ \mathrm{M\dot{K}}_{\lambda, p(\cdot)}^{\alpha, r), \theta}(\omega) $. We also obtained the boundedness of the $ m- $order multilinear fractional Hardy operator $ \mathcal{H}_{\beta, m} $ and its adjoint operator $ \mathcal{H}^{\ast}_{\beta, m} $ on weighted variable-exponent Herz-Morrey spaces $ \mathrm{M\dot{K}}_{q, p(\cdot)}^{\alpha, \lambda}(\omega) $.

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