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Keywords:
approximation error; generalized parameters; $L^p$ norm and Fourier coefficients
Summary:
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 $D$.
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