ON CERTAIN ESTIMATES FOR ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS

ON CERTAIN ESTIMATES FOR ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS

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...

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Veröffentlicht in:Taehan Suhakhoe hoebo 2023, Vol.60 (1), p.47-73
1. Verfasser: Daiqing, Zhang
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description 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.
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