On the maximum modulus principle for polynomials in a quasidisk
Main result: Let \(K\) be a compact subset of a bounded quasidisk \(G\subset \mathbb C\). Let \(p_n\) be a polynomial of degree \(\leq n\) such that \(m\,:=\,\inf_{z\in G}| p_n(z)| \,<\,\sup_{z\in G}| p_n(z)| \). Then \(\| p_n\| _K\,\leq\, (1-\alpha_n)\| p_n\| _G\), where \(\alpha_n \,=\,\alpha_n(G,K,m)\) depends on \(G,\,k\,,\,m\) and on the geometrical structure of \(\partial G\).
scientific article; zbMATH DE number 5010211