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Weighted bounds for the composition of singular integral operators with nonsmooth kernels on spaces of homogeneous type

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Abstract

Let \((X, d, \mu)\) be a space of homogeneous type. Let \(T_{1}, T_{2}\) be singular integral operators with nonsmooth kernels. By establishing sparse domination, we obtain quantitative boundedness for the composite operator \(T_{1}T_{2}\) on \(L^{p}(X, \omega)\) with \(\omega\in A_{p}\) and the weighted endpoint estimate for the composite operator \(T_{1}T_{2}\).

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    D. Liu & J. Zhao

  2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, P. R. China

    D. Liu

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  1. D. Liu
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  2. J. Zhao
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Correspondence to J. Zhao.

Additional information

This work is supported by National Natural Science Foundation of China (Grant Nos. 11471040 and 11761131002) and the National Key Research and Development Program of China (Grant No. 2020YFA0712900).

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Liu, D., Zhao, J. Weighted bounds for the composition of singular integral operators with nonsmooth kernels on spaces of homogeneous type. Acta Math. Hungar. 165, 169–191 (2021). https://doi.org/10.1007/s10474-021-01180-4

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  • DOI: https://doi.org/10.1007/s10474-021-01180-4

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