Year: 2025
Type: article
Abstract: In this article, we study the boundedness of operators of Hardy type on generalized central function spaces, such as the generalized central Hardy space \(\mathbf{HA}^{p,r}_\varphi(\mathbb{R}^n)\), the generalized central Morrey space \(\dot{\mathbf{M}}^{p,r}_\varphi (\mathbb{R}^n)\), and the generalized central Campanato space \(\dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\), with \(p\in(1,\infty)\), and \(\varphi(t):(0,\infty)\to (0,\infty)\). We first show that \(\mathbf{HA}^{p',r'}_\varphi (\mathbb{R}^n)\) is the predual of \(\dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\). After that, we investigate the boundedness of operators of Hardy type on those spaces. By duality, we obtain the boundedness characterization of function \(b\in \dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\) via the \(\dot{\textbf{M}}^{p,r}_\varphi (\mathbb{R}^n)\)-boundedness of commutator \([b,\mathcal{H}^*]\). For more information see https://ejde.math.txstate.edu/Volumes/2025/82/abstr.html
Author: Le Trung Nghia
Institution: Ton Duc Thang University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413240455