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arXiv · 2406.10896

Oscillation inequalities for Carleson--Dunkl operator

Wojciech Słomian
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Abstract

In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson--Dunkl operator on weighted $L^p(\mathbb{R},w(x)|x|^{2\alpha+1}{\rm d}x)$ spaces with power weights $w(x)=|x|^\beta$. As a result, we obtain oscillation estimates for the standard Carleson operator on $L_{\rm rad}^p(\mathbb{R}^n,|x|^\beta{\rm d}x)$. As a byproduct, we obtain a transference principle for radial multipliers on $L_{\rm rad}^p$ spaces, in the spirit of the Rubio de Francia transference principle.

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Wojciech Słomian. 2024-06-16. Oscillation inequalities for Carleson--Dunkl operator. https://doi.org/10.1007/s12215-025-01237-1

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