Geodesic
A direct theorem for strictly convex domains in~$\mathbb C^n$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 151-173

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For a strictly convex $C^2$-domain $\Omega\subset\mathbb C^n$ and a function $f\in\Lambda^a(\Omega)$ holomorphic in $\Omega$, we construct polynomials $P_n$, $\deg P_n\le N$, such that $|f(z)-P_n(z)|\le CN^{-a}$, $z\in\overline\Omega$. Bibliography: 12 titles. 
@article{ZNSL_1993_206_a12,
     author = {N. A. Shirokov},
     title = {A direct theorem for strictly convex domains in~$\mathbb C^n$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--173},
     publisher = {mathdoc},
     volume = {206},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a12/}
}
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N. A. Shirokov. A direct theorem for strictly convex domains in~$\mathbb C^n$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 151-173. http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a12/