A right inverse of Cauchy–Riemann operator $\protect \bar{\partial }^k+a$ in the weighted Hilbert space $L^2(\protect \mathbb{C},e^{-|z|^2})$

Dai, Shaoyu; Pan, Yifei

doi:10.5802/afst.1686

A right inverse of Cauchy–Riemann operator

{\bar{\partial}}^{k} + a

in the weighted Hilbert space

L^{2} (ℂ, e^{- {| z |}^{2}})

Dai, Shaoyu ¹ ; Pan, Yifei ²

¹ Department of Mathematics, Jinling Institute of Technology, Nanjing 211169, China
² Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne 46805-1499, USA

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 3, pp. 619-632.

Résumé
Abstract

Nous utilisons la méthode des estimées $L^{2}$ de Hörmander pour les équations de Cauchy–Riemann pour étudier un opérateur différentiel simple ${\bar{\partial}}^{k} + a$ de tout ordre (fermé et densément défini) dans l’espace de Hilbert à poids $L^{2} (ℂ, e^{- {| z |}^{2}})$ . Nous montrons l’existence d’un inverse à droite qui est borné.

Using Hörmander $L^{2}$ method for Cauchy–Riemann equations from complex analysis, we study a simple differential operator ${\bar{\partial}}^{k} + a$ of any order (densely defined and closed) in the weighted Hilbert space $L^{2} (ℂ, e^{- {| z |}^{2}})$ and prove the existence of a right inverse that is bounded.

Reçu le : 2019-07-11
Accepté le : 2019-10-02
Publié le : 2021-10-26

DOI : 10.5802/afst.1686

Affiliations des auteurs :

Dai, Shaoyu ¹ ; Pan, Yifei ²

¹ Department of Mathematics, Jinling Institute of Technology, Nanjing 211169, China
² Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne 46805-1499, USA

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     title = {A right inverse of {Cauchy{\textendash}Riemann} operator $\protect \bar{\partial }^k+a$ in the weighted {Hilbert} space $L^2(\protect \mathbb{C},e^{-|z|^2})$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {619--632},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Dai, Shaoyu; Pan, Yifei. A right inverse of Cauchy–Riemann operator $\protect \bar{\partial }^k+a$ in the weighted Hilbert space $L^2(\protect \mathbb{C},e^{-|z|^2})$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 3, pp. 619-632. doi : 10.5802/afst.1686. https://www.numdam.org/articles/10.5802/afst.1686/

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