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A bilinear fractional
integral operator for Euler–Riesz systems
Nuno J. Alves, Loukas Grafakos and Athanasios E. Tzavaras |
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Vol. 19 (2026), No. 4, 823–846
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DOI: 10.2140/apde.2026.19.823
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Abstract |
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We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in the integrability analysis of a tensor-valued bilinear fractional integral operator associated with Euler–Riesz systems modeling mean-field interactions induced by a singular kernel. The tensorial operator arises from a reformulation of the Euler–Riesz system that yields a gain in integrability for finite-energy solutions through compensated integrability. Additionally, for smooth periodic solutions of the reformulated system, we derive a stability result. |
Keywords
Marcinkiewicz interpolation, Euler–Riesz equations,
compensated integrability
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Mathematical Subject Classification
Primary: 35Q35, 42B20, 42B37
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Milestones
Received: 12 August 2024
Revised: 7 April 2025
Accepted: 2 August 2025
Published: 17 May 2026
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Authors |
| Nuno J. Alves | |
| Faculty of Mathematics University of Vienna Vienna Austria |
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| Loukas Grafakos | |
| Department of Mathematics University of Missouri Columbia, MO United States |
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| Athanasios E. Tzavaras | |
| King Abdullah University of Science
and Technology Thuwal Saudi Arabia |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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