Geodesic
Polynomial approximations in a convex domain in $\mathbb C^n$ with the exponential decaying inside
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 154-171 
N. A. Shirokov. Polynomial approximations in a convex domain in $\mathbb C^n$ with the exponential decaying inside. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 154-171. http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a9/
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     author = {N. A. Shirokov},
     title = {Polynomial approximations in a convex domain in $\mathbb C^n$ with the exponential decaying inside},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--171},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\Omega$ be convex domain in $\mathbb C^n$ satisfying some restrictions, $f$ be holomorphic in $\Omega$ and continuons in $\overline{\Omega}$, $f\in H^{r+\omega}(\overline{\Omega})$ with a modulus of continuity $\omega$. Then there are polynomials $P_N$, $\deg P_N\le N$, such that $ |f(z)-P_N(z)| \le cN^{-r}\omega(\frac{1}{N})$, $z \in \overline{\Omega}$, and $|f(z)-P_N(z)| \le c \exp(-c_0(K)N)$, $z\in K\subset \Omega$, where $K$ is any compact strictly inside $\Omega$.

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