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

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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.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11671185, 11571306, 11671363, 11771195) and the Natural Science Foundation of Shandong Province (Grant Nos. ZR2018PA004, ZR2016AB07, ZR2018LA002, ZR2019YQ04).

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Authors and Affiliations

  1. Department of Mathematics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Rui Bu & Yandan Zhang

  2. School of Mathematics and Statistics, Linyi University, Linyi, 276005, China

    Zunwei Fu

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, 273100, China

    Zunwei Fu

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  1. Rui Bu
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  2. Zunwei Fu
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  3. Yandan Zhang
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Correspondence to Zunwei Fu.

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Bu, R., Fu, Z. & Zhang, Y. Weighted estimates for bilinear square functions with non-smooth kernels and commutators. Front. Math. China 15, 1–20 (2020). https://doi.org/10.1007/s11464-020-0822-4

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  • DOI: https://doi.org/10.1007/s11464-020-0822-4

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