Geodesic
On the approximation of entire functions over Carathéodory domains
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 681-689

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Let $D$ be a Carathéodory domain. For $1\leq p\leq \infty $, let $L^p(D)$ be the class of all functions $f$ holomorphic in $D$ such that $\|f\|_{D,p}=[\frac{1}{A}\int\int_{D}^{}|f(z)|^p\,dx\,dy]^{1/p}\infty $, where $A$ is the area of $D$. For $f\in L^p(D)$, set $$ E_n^p(f)=\inf _{t\in \pi _n} \|f-t\|_{D,p}\,; $$ $\pi _n$ consists of all polynomials of degree at most $n$. In this paper we study the growth of an entire function in terms of approximation error in $L^p$-norm on $D$.
Classification : 30D15, 30E10
Keywords: approximation error; generalized parameters; $L^p$ norm and Fourier coefficients 
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     author = {Kumar, D. and Kasana, H. S.},
     title = {On the approximation of entire functions over {Carath\'eodory} domains},
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Kumar, D.; Kasana, H. S. On the approximation of entire functions over Carathéodory domains. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 681-689. http://geodesic.mathdoc.fr/item/CMUC_1994__35_4_a8/