We show that the spaces of --subharmonic and --subharmonic functions differ in sufficiently high dimensions. We also prove that the Monge–Ampère type operator associated to the space of -plurisubharmonic functions does not allow an integral comparison principle except in the classical cases and . These answer in the negative two problems posed by A. Sadullaev.
Nous montrons que les fonctions --sousharmoniques et --sousharmoniques diffèrent en dimension suffisamment grande. Nous prouvons que l’opérateur de type Monge–Ampère associé à l’espace des fonctions -plurisousharmoniques ne permet pas un principe de comparaison intégral sauf dans les cas classiques et . Cela répond par la négative à deux problèmes posés par A. Sadullaev.
Sławomir Dinew 1
@article{AFST_2022_6_31_3_995_0, author = {S{\l}awomir Dinew}, title = {$m$-subharmonic and $m$-plurisubharmonic functions: on two problems of {Sadullaev}}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {995--1009}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 31}, number = {3}, year = {2022}, doi = {10.5802/afst.1711}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1711/} }
TY - JOUR AU - Sławomir Dinew TI - $m$-subharmonic and $m$-plurisubharmonic functions: on two problems of Sadullaev JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2022 SP - 995 EP - 1009 VL - 31 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1711/ DO - 10.5802/afst.1711 LA - en ID - AFST_2022_6_31_3_995_0 ER -
%0 Journal Article %A Sławomir Dinew %T $m$-subharmonic and $m$-plurisubharmonic functions: on two problems of Sadullaev %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2022 %P 995-1009 %V 31 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1711/ %R 10.5802/afst.1711 %G en %F AFST_2022_6_31_3_995_0
Sławomir Dinew. $m$-subharmonic and $m$-plurisubharmonic functions: on two problems of Sadullaev. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, AMAZER, 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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