Sharp Remez-type inequalities of various metrics for differentiable periodic functions, polynomials, and splines

• Datum: 2017
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2017
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1685
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove a sharp Remez-type inequality of various metrics $$\| x\| q \leq \| \varphi_r\| q \biggl\{\frac{\| x\|_{L_p([0,2\pi ]\setminus B)}}{\|\varphi r\|_{ L_p([0,2\pi ]\setminus B_1)}}\biggr\}^{\alpha } \| x(r)\|^{1 - \alpha}_{ \infty} ,\; q > p > 0, \;\alpha = (r + 1/q)/(r + 1/p...