Comptes Rendus
Analyse harmonique
Optimal weak estimates for Riesz potentials
Liang Huang1 ; Hanli Tang2 
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
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<f∈L 1 (ℝ 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 s→0.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.479
Classification : 42B20
Mots clés : 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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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