Multilinear singular integral operators with generalized kernels and their multilinear commutators

Springer Science and Business Media LLC - Tập 33 - Trang 1443-1462 - 2017
Yan Lin1, Ya Yuan Xiao2
1School of Sciences, China University of Mining and Technology, Beijing, P. R. China
2Department of Mathematical Sciences, Ball State University, Muncie, USA

Tóm tắt

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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1443-1462

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