On the canonical solution of $\protect \,\protect \,\protect \overline{\protect \!\partial }$ on polydisks

Muzhi Jin; Yuan Yuan

doi:10.5802/crmath.51

Analyse complexe, Équations aux dérivées partielles

On the canonical solution of

\bar{\partial}

on polydisks

Muzhi Jin ¹ ; Yuan Yuan ¹

¹ Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA

Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 523-528.

Résumé

We observe that the recent result of Chen–McNeal [6] implies that the canonical solution operator satisfies Sobolev estimates with a loss of $n - 2$ derivatives on the polydisk $Δ^{n}$ and particularly is exact regular on $Δ^{2}$ .

Reçu le : 2019-10-03
Révisé le : 2020-03-04
Accepté le : 2020-04-13
Publié le : 2020-09-14

DOI : 10.5802/crmath.51

Affiliations des auteurs :

Muzhi Jin ¹ ; Yuan Yuan ¹

¹ Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Muzhi Jin and Yuan Yuan},
     title = {On the canonical solution of $\protect \,\protect \,\protect \overline{\protect \!\partial }$ on polydisks},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {523--528},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {5},
     year = {2020},
     doi = {10.5802/crmath.51},
     language = {en},
}

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Muzhi Jin; Yuan Yuan. On the canonical solution of $\protect \,\protect \,\protect \overline{\protect \!\partial }$ on polydisks. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 523-528. doi : 10.5802/crmath.51. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.51/

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