Bulletin of the Korean Mathematical Society (대한수학회보)

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ON CERTAIN ESTIMATES FOR ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS

  • Daiqing, Zhang (School of Computer Science and Mathematics Fujian University of Technology)
  • Received : 2021.11.24
  • Accepted : 2022.06.24
  • Published : 2023.01.31
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Abstract

This paper is devoted to establishing certain Lp bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by h ∈ ∆γ(ℝ+) and Ω ∈ Wℱβ(Sn-1) for some γ, β ∈ (1, ∞]. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley g*λ functions and area integrals are also presented.

Keywords

Acknowledgement

This work was supported by the Natural Science Foundation of University Union of Science and Technology Department of Fujian Province (No. 2019J01784).

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