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Weighted estimates for Marcinkiewicz integrals with applications to angular integrability

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Abstract

We establish the weighted estimates for the parametric Marcinkiewicz integral operators with rough kernels along “polynomial curves” on \(\mathbb {R}^n\). As applications, we obtain that the above operators are bounded on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces and on the vector-valued function spaces. Particularly, the above bounds are independent of the coefficients of the polynomials in the definition of the operators.

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Acknowledgements

The authors want to express their sincerely thanks to the referees for their valuable remarks and suggestions, which made this paper more readable.

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Authors and Affiliations

  1. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Feng Liu

  2. Department of Mathematics, Mudanjiang Normal University, Mudanjiang, 157011, Heilongjiang, People’s Republic of China

    Pu Zhang

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  1. Feng Liu
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  2. Pu Zhang
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Correspondence to Feng Liu.

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The first author was partly supported by the NNSF of China (No. 11701333) and SP-OYSTTT-CMSS (No. Sxy2016K01). The second author was supported partly by NNSF of China (No. 11571160).

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Liu, F., Zhang, P. Weighted estimates for Marcinkiewicz integrals with applications to angular integrability. Anal.Math.Phys. 11, 100 (2021). https://doi.org/10.1007/s13324-021-00535-y

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  • DOI: https://doi.org/10.1007/s13324-021-00535-y

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