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Boundedness of commutators of \(\theta \)-type Calderón–Zygmund operators on generalized weighted Morrey spaces over RD-spaces

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Abstract

Let \(({\mathcal {X}},\,d,\,\mu )\) be an RD-space. In this paper, under some slightly weaker conditions, we establish the boundedness of the commutators generated by the \(\theta \)-type Calderón–Zygmund operators and BMO functions on the generalized weighted Morrey spaces \(\widetilde{{\mathcal {M}}}^{p,\,\psi }(\omega )\) and the generalized weighted Morrey spaces of \(L\ln L\) type \(\widetilde{{\mathcal {M}}}^{1,\,\psi }_{L\ln L}(\omega )\) over \(({\mathcal {X}},\,d,\,\mu )\).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11571039) and Bei**g Training Program of Innovation (Grant No. bj202010019213). All authors wish to express their sincere thanks to the referees for a careful reading of the manuscript and for many valuable suggestions and remarks that improved the presentation of this paper. Indeed, following one of the referees’ comments, we got the equivalence of the conditions (1.11) and (1.12), which allowed us to use the same conditions as establishing the boundedness of \(T_\theta \) when establishing the boundedness of the commutator \([b,T_\theta ]\).

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  1. College of Science, China Agricultural University, Bei**g, 100083, People’s Republic of China

    Qiumeng Li, Haibo Lin & **nyu Wang

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  1. Qiumeng Li
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  2. Haibo Lin
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Correspondence to Haibo Lin.

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Li, Q., Lin, H. & Wang, X. Boundedness of commutators of \(\theta \)-type Calderón–Zygmund operators on generalized weighted Morrey spaces over RD-spaces. Anal.Math.Phys. 12, 5 (2022). https://doi.org/10.1007/s13324-021-00614-0

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