Kolmogorov-type inequalities for mixed derivatives of functions of many variables

• Date: 2004
• Main Authors: Babenko, V. F., Korneichuk, N. P., Pichugov, S. A., Бабенко, В. Ф., Корнейчук, Н. П., Пичугов, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3779
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $γ = (γ_1 ,..., γ_d )$ be a vector with positive components and let $D^γ$ be the corresponding mixed derivative (of order $γ_j$ with respect to the $j$ th variable). In the case where $d > 1$ and $0 < k < r$ are arbitrary, we prove that $$\sup_{x \in L^{r\gamma}_{\infty}(T^d...