Hardy and BMO spaces associated with new Muckenhoupt‐type weights in the Bessel setting

Qingdong Guo, Ji Li and Dongyong Yang

Mathematische Nachrichten, 2025, vol. 298, issue 12, 3639-3685

Abstract: We introduce the Hardy spaces Hw1(R+)$H^{1}_{w}(\mathbb {R}_{+})$ with w$w$ in the new weights A∼p,λ$\widetilde{A}_{p,\lambda }$, 1≤p 0.$$\begin{equation*} \hspace*{50pt}\Delta _{\lambda }:=-x^{-2\lambda }\frac{d}{dx}x^{2\lambda }\frac{d}{dx},\qquad x\in {\mathbb {R}_{+}:=(0,\infty)},\,\lambda >0. \end{equation*}$$Then we establish equivalent characterizations of Hw1(R+)$H^{1}_{w}(\mathbb {R}_{+})$ via atoms and maximal functions. We also introduce the weighted BMO$\mathrm{BMO}$ space BMOw(R+)$\mathrm{BMO}_{w}(\mathbb {R}_{+})$ and establish the duality of Hw1(R+)$H^{1}_{w}(\mathbb {R}_{+})$ and BMOw(R+)$\mathrm{BMO}_{w}(\mathbb {R}_{+})$ for w∈A∼1,λ$w\in {\widetilde{A}_{1,\lambda }}$. As an application, we show a w$w$‐Carleson characterization of BMOw(R+)$\mathrm{BMO}_{w}(\mathbb {R}_{+})$ with w∈A∼1,λ$w\in {\widetilde{A}_{1,\lambda }}$ via the Poisson semigroup e−tΔλ$e^{-t\sqrt {\Delta _{\lambda }}}$.

Date: 2025
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