Contraction property of Fock type space of log-subharmonic functions in $\mathbb{R}^m$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916330400120832 |
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| author | Kalaj, David |
| author_facet | Kalaj, David |
| contents | We prove a contraction property of Fock type spaces $\mathcal{L}_α^p$ of log-subharmonic functions in $\mathbb{R}^n$. To prove the result, we demonstrate a certain monotonic property of measures of the superlevel set of the function $u(x) = |f(x)|^p e^{-\fracα{2} p |x|^2}$, provided that $f$ is a certain log-subharmonic function in $\mathbb{R}^m$. The result recover a contraction property of holomorphic functions in the Fock space $\mathcal{F}_α^p$ proved by Carlen in \cite{carlen}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contraction property of Fock type space of log-subharmonic functions in $\mathbb{R}^m$ Kalaj, David Complex Variables We prove a contraction property of Fock type spaces $\mathcal{L}_α^p$ of log-subharmonic functions in $\mathbb{R}^n$. To prove the result, we demonstrate a certain monotonic property of measures of the superlevel set of the function $u(x) = |f(x)|^p e^{-\fracα{2} p |x|^2}$, provided that $f$ is a certain log-subharmonic function in $\mathbb{R}^m$. The result recover a contraction property of holomorphic functions in the Fock space $\mathcal{F}_α^p$ proved by Carlen in \cite{carlen}. |
| title | Contraction property of Fock type space of log-subharmonic functions in $\mathbb{R}^m$ |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2407.06029 |