Multilinear singular integral operators with generalized kernels and their multilinear commutators |
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Authors: | Yan Lin Ya Yuan Xiao |
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Institution: | 1. School of Sciences, China University of Mining and Technology, Beijing 100083, P. R. China;
2. Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA |
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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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Keywords: | Multilinear singular integral sharp maximal function multilinear commutator BMO function |
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