Bulletin of the Korean Mathematical Society (대한수학회보)

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A NOTE ON GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS

  • Liu, Feng (College of Mathematics and Systems Science Shandong University of Science and Technology)
  • Received : 2018.01.16
  • Accepted : 2019.07.08
  • Published : 2019.09.30
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Abstract

In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class ${\mathcal{F}}_{\beta}(S^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g^*_{\lambda}$-functions and area integrals are also presented.

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References

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