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

• Datum: 2023
• Hauptverfasser: Babenko, V., Kovalenko, O., Parfinovych, N., Бабенко, Владислав, Бабенко, Віра, Коваленко, Oлег, Парфінович, Наталія
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2023
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/7680
• Назва журналу: 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...