Weak-type endpoint bounds for Bochner–Riesz means for the Hermite operator

Peng Chen; Ji Li; Lesley Ward; Lixin Yan

doi:10.5802/crmath.265

Analyse harmonique

Weak-type endpoint bounds for Bochner–Riesz means for the Hermite operator

Peng Chen ^1,² ; Ji Li ³ ; Lesley Ward ² ; Lixin Yan ¹

¹ Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P.R. China
² School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes SA 5095, Australia
³ Department of Mathematics, Macquarie University, NSW 2109, Australia

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 111-126.

Résumé

We obtain weak-type $(p, p)$ endpoint bounds for Bochner–Riesz means for the Hermite operator $H = - Δ + {| x |}^{2}$ in $ℝ^{n}, n \geq 2$ and for other related operators, for $1 \leq p \leq 2 n / (n + 2)$ , extending earlier results of Thangavelu and of Karadzhov.

Reçu le : 2019-06-24
Révisé le : 2020-03-10
Accepté le : 2021-08-23
Publié le : 2022-02-15

DOI : 10.5802/crmath.265

Classification : 42B15, 42B08, 42C10

Affiliations des auteurs :

Peng Chen ^{1, 2} ; Ji Li ³ ; Lesley Ward ² ; Lixin Yan ¹

¹ Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P.R. China
² School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes SA 5095, Australia
³ Department of Mathematics, Macquarie University, NSW 2109, Australia

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Peng Chen and Ji Li and Lesley Ward and Lixin Yan},
     title = {Weak-type endpoint bounds for {Bochner{\textendash}Riesz} means for the {Hermite} operator},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {111--126},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.265},
     language = {en},
}

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Peng Chen; Ji Li; Lesley Ward; Lixin Yan. Weak-type endpoint bounds for Bochner–Riesz means for the Hermite operator. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 111-126. doi : 10.5802/crmath.265. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.265/

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