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arXiv · 2303.07952

The Riesz Transform and Fractional Integral Operators in the Bessel Setting

Jorge J. Betancor·Xuan Thinh Duong·Ming-Yi Lee·Ji Li·Brett D. Wick
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Abstract

Fix $\lambda>0$. Consider the Bessel operator $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ on $\mathbb{R_+}$, where $\mathbb{R_+}:=(0,\infty)$ and $dm_\lambda:=x^{2\lambda}dx$ with $dx$ the Lebesgue measure. We provide a deeper study of the Bessel Riesz transform and fractional integral operator via the related Besov and Triebel--Lizorkin spaces associated with $\triangle_\lambda$. Moreover, we investigate some possible characterization of the commutator of fractional integral operator, which was missing in the literature of the Bessel setting.

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Jorge J. Betancor, Xuan Thinh Duong, Ming-Yi Lee, Ji Li, Brett D. Wick. 2023-03-14. The Riesz Transform and Fractional Integral Operators in the Bessel Setting. https://arxiv.org/abs/2303.07952

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