2024 / March Volume 19 No.1
Range of the Hessian operator on some weighted $m$−subharmonic classes
Published Date |
2024 / March
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Title | Range of the Hessian operator on some weighted $m$−subharmonic classes |
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Pagination | 15-28 |
Abstract | In this paper we study the range of the complex Hessian operator on some weighted classes . For a given measure $\nu$ and a negative real function $\chi$ we prove that $\chi(\mathcal{E}_{m,\chi})\subset \mathbb{L}^1(\Omega, d\nu)$ if and only if the measure $\nu$ can be written as the Hessian of a unique function in $\mathcal{E}_{m,\chi}$. We extend also this result to an energy class with a given boundary data. |
DOI | |
AMS Subject Classification |
32U40, 32U15, 32U05
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Received |
2024-01-21
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