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Multilinear singular integral operators with generalized kernels and their multilinear commutators

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Abstract

In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calderón–Zygmund operators and multilinear Calderón–Zygmund operators with Dini type kernels.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Sciences, China University of Mining and Technology, Beijing, 100083, P. R. China

    Yan Lin

  2. Department of Mathematical Sciences, Ball State University, Muncie, IN, 47306, USA

    Ya Yuan Xiao

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  1. Yan Lin
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  2. Ya Yuan Xiao
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Correspondence to Yan Lin.

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Supported by the National Natural Science Foundation of China (Grant No. 11671397), the Fundamental Research Funds for the Central Universities (Grant No. 2009QS16), the State Scholarship Fund of China and the Yue Qi Young Scholar of China University of Mining and Technology (Beijing)

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Lin, Y., Xiao, Y.Y. Multilinear singular integral operators with generalized kernels and their multilinear commutators. Acta. Math. Sin.-English Ser. 33, 1443–1462 (2017). https://doi.org/10.1007/s10114-017-7051-0

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