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Commutators of integral operators with variable kernels on Hardy spaces

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Abstract

LetT Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, TΩ,α] be the commutator generated by TΩ,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, TΩ,α] on the Hardy spaces, under some assumptions such as theL r-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators\(T_{\tilde \Omega ,\alpha } (0 \leqslant \alpha< n)\). The smoothness conditions imposed on\(\tilde \Omega \) are weaker than the corresponding known results.

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Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, People’s Republic of China

    Pu Zhang

  2. Department of Mathematics, Qingdao University, 266071, Qingdao, People’s Republic of China

    Kai Zhao

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  1. Pu Zhang
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  2. Kai Zhao
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Correspondence to Pu Zhang.

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Zhang, P., Zhao, K. Commutators of integral operators with variable kernels on Hardy spaces. Proc. Indian Acad. Sci. (Math. Sci.) 115, 399–410 (2005). https://doi.org/10.1007/BF02829802

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  • DOI: https://doi.org/10.1007/BF02829802

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