Comptes Rendus
Harmonic analysis
Optimal weak estimates for Riesz potentials
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1123-1131.

In this note we prove a sharp reverse weak estimate for Riesz potentials

I s (f) L n n-s, γ s v n n-s n f L 1 for0<fL 1 ( n ),

where γ s =2 -s π -n 2 Γ(n-s 2) Γ(s 2). We also consider the behavior of the best constant 𝒞 n,s of weak type estimate for Riesz potentials, and we prove 𝒞 n,s =O(γ s s) as s0.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.479
Classification: 42B20
Keywords: Riesz potentials, sharp constant, optimal estimate

Liang Huang 1; Hanli Tang 2

1 School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2 Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Liang Huang; Hanli Tang. Optimal weak estimates for Riesz potentials. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1123-1131. doi : 10.5802/crmath.479. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.479/

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