Some sharp Landau-Kolmogorov–Nagy-type inequalities in Sobolev spaces of multivariate functions

• Date: 2023
• Main Authors: Babenko, V., Kovalenko, O., Parfinovych, N., Бабенко, Владислав, Бабенко, Віра, Коваленко, Oлег, Парфінович, Наталія
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2023
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7680
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For a function $f$ from the Sobolev space $W^{1,p}(C),$ where $C\subset R^d$ is an open convex cone, we establish a sharp inequality  estimating $\| f\|_{L_{\infty}}$ via the $L_{p}$-norm of its gradient and a seminorm of the function. With the help of this inequa...