- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Markov-Bernstein type inequalities for polynomials Bull. Korean Math. Soc. 1999 Vol. 36, No. 1, 63-78 K. H. Kwon and D. W. Lee KAIST, Kyungpook National University Abstract : Let $\mu(x)$ be an increasing function on the real line with finite moments of all orders. We show that for any linear operator $T$ on the space of polynomials and any integer $n\ge 0$, there is a constant $\gamma_n(T) \ge 0$, independent of $p(x)$, such that $$\| Tp \| \le \gamma_n(T) \, \| p \| ,$$ for any polynomial $p(x)$ of degree $\le n$, where $$\| p \| = \biggl \{ \int_{-\infty}^\infty | p (x) |^2 \, d \mu(x) \biggr \} ^{\frac 1 2} .$$ We find a formula for the best possible value $\Gamma_n(T)$ of $\gamma_n(T)$ and estimations for $\Gamma_n(T)$. We also give several illustrating examples when $T$ is a differentiation or a difference operator and $d\mu(x)$ is an orthogonalizing measure for classical or discrete classical orthogonal polynomials. Keywords : Markov-Bernstein type inequality, orthonormal polynomials, linear operator MSC numbers : 33C45, 41A17, 41A44 Full-Text :