Weighted estimates for bilinear square functions with non-smooth kernels and commutators

doi:10.1007/s11464-020-0822-4

Front. Math. China

2020, Vol. 15

Issue (1) : 1-20 https://doi.org/10.1007/s11464-020-0822-4

RESEARCH ARTICLE

Weighted estimates for bilinear square functions with non-smooth kernels and commutators

Rui BU¹, Zunwei FU^2,³(

), Yandan ZHANG¹

¹. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China
². School of Mathematics and Statistics, Linyi University, Linyi 276005, China
³. School of Mathematical Sciences, Qufu Normal University, Qufu 273100, China

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Abstract

Under weaker conditions on the kernel functions, we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces. Moreover, we investigate the weighted boundedness of the commutators of bilinear square functions (with symbols which are BMO functions and their weighted version, respectively) on the product of Lebesgue spaces. As an application, we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley g-functions.

Keywords Bilinear square function non-smooth kernel weight commutator BMO function

Corresponding Author(s): Zunwei FU

Issue Date: 09 March 2020

Cite this article:

Rui BU,Zunwei FU,Yandan ZHANG. Weighted estimates for bilinear square functions with non-smooth kernels and commutators[J]. Front. Math. China, 2020, 15(1): 1-20.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0822-4
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/1

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