Year: 2026
Type: article
Abstract: In this paper, we investigate the weighted product Hardy spaces $H_w^{p}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$. Under some conditions on the weight, we prove that the Riesz potential operator $I_\alpha$ is bounded from $L_w^{p}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$ to $L_{w^{q/p}}^{q}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$ when $\alpha=(\alpha_1, \alpha_2)$ and $\frac{1}{p}- \frac{1}{q} = \frac{\alpha_1}{d_1} =\frac{\alpha_2}{d_2}$. We also verify the boundedness of $I_\alpha$ from $H_w^{p}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$ to $H_{w^{q/p}}^{q}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$ and from $H_w^{p}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$ to $L_{w^{q/p}}^{q}(\mathbb{R}^{d_1}\times \mathbb{R}^{d_2})$. We consider similar questions for the maximal fractional operator, too.
DOI: 10.33205/cma.1902994
Author: Ferenc Weisz
Institution: Eötvös Loránd University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7164892251