Riesz potential on weighted product Hardy spaces and inequalities

Ferenc Weisz

doi:10.33205/cma.1902994

Riesz potential on weighted product Hardy spaces and inequalities

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.

Keywords

References

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Details

Primary Language

English

Subjects

Lie Groups, Harmonic and Fourier Analysis

Journal Section

Research Article

Authors

Ferenc Weisz ^*
0000-0002-7766-2745
Hungary

Early Pub Date

June 16, 2026

Publication Date

-

Submission Date

March 4, 2026

Acceptance Date

June 12, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.33205/cma.1902994

IZ

https://izlik.org/JA86BK56UK

Cite

RIS / Bibtex

APA

Weisz, F. (2026). Riesz potential on weighted product Hardy spaces and inequalities. Constructive Mathematical Analysis, Advanced Online Publication. https://doi.org/10.33205/cma.1902994

AMA

1.Weisz F. Riesz potential on weighted product Hardy spaces and inequalities. CMA. 2026;(Advanced Online Publication). doi:10.33205/cma.1902994

Chicago

Weisz, Ferenc. 2026. “Riesz Potential on Weighted Product Hardy Spaces and Inequalities”. Constructive Mathematical Analysis, no. Advanced Online Publication. https://doi.org/10.33205/cma.1902994.

EndNote

Weisz F (June 1, 2026) Riesz potential on weighted product Hardy spaces and inequalities. Constructive Mathematical Analysis Advanced Online Publication

IEEE

[1]F. Weisz, “Riesz potential on weighted product Hardy spaces and inequalities”, CMA, no. Advanced Online Publication, June 2026, doi: 10.33205/cma.1902994.

ISNAD

Weisz, Ferenc. “Riesz Potential on Weighted Product Hardy Spaces and Inequalities”. Constructive Mathematical Analysis. Advanced Online Publication (June 1, 2026). https://doi.org/10.33205/cma.1902994.

JAMA

1.Weisz F. Riesz potential on weighted product Hardy spaces and inequalities. CMA. 2026. doi:10.33205/cma.1902994.

MLA

Weisz, Ferenc. “Riesz Potential on Weighted Product Hardy Spaces and Inequalities”. Constructive Mathematical Analysis, no. Advanced Online Publication, June 2026, doi:10.33205/cma.1902994.

Vancouver

1.Ferenc Weisz. Riesz potential on weighted product Hardy spaces and inequalities. CMA. 2026 Jun. 1;(Advanced Online Publication). doi:10.33205/cma.1902994