Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chang, Chin-Huei; Lee, Hsuan-Pei

Geodesic

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Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chang, Chin-Huei ; Lee, Hsuan-Pei

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 1, pp. 21-37

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Résumé

The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for $C^{k}$ $\bar{\partial}$ -closed forms at the critical degree, $0 \leq k \leq \infty$ (Theorem 1.1). Part of Frenkel’s lemma in $C^{k}$ category is also proved.

MR Zbl

Classification : 32A26, 32W10

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     author = {Chang, Chin-Huei and Lee, Hsuan-Pei},
     title = {Hartogs theorem for forms : solvability of {Cauchy-Riemann} operator at critical degree},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {21--37},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {1},
     year = {2006},
     mrnumber = {2240164},
     zbl = {1170.32303},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_1_21_0/}
}

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Chang, Chin-Huei; Lee, Hsuan-Pei. Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 1, pp. 21-37. http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_1_21_0/