Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions

• Date: 2010
• Main Authors: Babenko, V. F., Parfinovych, N. V., Pichugov, S. A., Бабенко, В. Ф., Парфінович, Н. В., Пічугов, С. О.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2869
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $C(\mathbb{R}^m)$ be the space of bounded and continuous functions $x: \mathbb{R}^m → \mathbb{R}$ equipped with the norm $∥x∥_C = ∥x∥_{C(\mathbb{R}^m)} := \sup \{ |x(t)|:\; t∈ \mathbb{R}^m\}$ and let $e_j,\; j = 1,…,m$, be a standard basis in $\mathbb{R}^m$. Given moduli of continuity $ω_j,\; j...