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m-subharmonic and m-plurisubharmonic functions: on two problems of Sadullaev
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 995-1009.

We show that the spaces of A-m-subharmonic and B-m-subharmonic functions differ in sufficiently high dimensions. We also prove that the Monge–Ampère type operator m associated to the space of m-plurisubharmonic functions does not allow an integral comparison principle except in the classical cases m=1 and m=n. These answer in the negative two problems posed by A. Sadullaev.

Nous montrons que les fonctions A-m-sousharmoniques et B-m-sousharmoniques diffèrent en dimension suffisamment grande. Nous prouvons que l’opérateur de type Monge–Ampère m associé à l’espace des fonctions m-plurisousharmoniques ne permet pas un principe de comparaison intégral sauf dans les cas classiques m=1 et m=n. Cela répond par la négative à deux problèmes posés par A. Sadullaev.

Published online:
DOI: 10.5802/afst.1711
Classification: 32W20,  32U15,  32Q15
Sławomir Dinew 1

1 Department of Mathematics and Computer Science, Jagiellonian University, 30-409 Kraków, ul. Lojasiewicza 6, Poland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {$m$-subharmonic and $m$-plurisubharmonic functions: on two problems of {Sadullaev}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Sławomir Dinew. $m$-subharmonic and $m$-plurisubharmonic functions: on two problems of Sadullaev. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 995-1009. doi : 10.5802/afst.1711. https://afst.centre-mersenne.org/articles/10.5802/afst.1711/

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