The boundedness of Calderón–Zygmund operators associated with admissible functions on spaces of homogeneous type in weighted Morrey-type spaces

Nan Zhao; Nan Zhao

doi:10.3934/cam.2026032

Communications in Analysis and Mechanics

2026, Volume 18, Issue 4: 783-805. doi: 10.3934/cam.2026032

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Research article

The boundedness of Calderón–Zygmund operators associated with admissible functions on spaces of homogeneous type in weighted Morrey-type spaces

Nan Zhao ^,

School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, P.R. China

Received: 21 January 2026 Revised: 18 August 2026 Accepted: 15 September 2026 Published: 14 October 2026
42B20, 42B35

In this paper, we introduce a class of weighted Morrey-type spaces associated with admissible functions on spaces of homogeneous type, and establish the boundedness of Calderón–Zygmund operators related to admissible functions and their commutators on these spaces. The results of this paper extend many known conclusions and remain novel even in the standard Euclidean setting.
- $ A^{\rho}_{p} $ weights,
- weighted Morrey-type spaces,
- Calderón–Zygmund operators,
- bounded mean oscillations,
- commutators
Citation: Nan Zhao. The boundedness of Calderón–Zygmund operators associated with admissible functions on spaces of homogeneous type in weighted Morrey-type spaces[J]. Communications in Analysis and Mechanics, 2026, 18(4): 783-805. doi: 10.3934/cam.2026032

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Abstract

In this paper, we introduce a class of weighted Morrey-type spaces associated with admissible functions on spaces of homogeneous type, and establish the boundedness of Calderón–Zygmund operators related to admissible functions and their commutators on these spaces. The results of this paper extend many known conclusions and remain novel even in the standard Euclidean setting.

References

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