Comparison of exact constants in Kolmogorov-type inequalities for periodic and nonperiodic functions of many variables

• Date: 2006
• Main Authors: Babenko, V. F., Churilova, M. S., Бабенко, В. Ф., Чурилова, М. С.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3478
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the correlation between the constants $K(ℝ^n)$ and $K(T^n)$, where $$K(G^n ): = \mathop {\sup }\limits_{\mathop {\prod _{i = 1}^n \left\| {D_i^{l_i } f} \right\|_{L_p (G^n )} \ne 0}\limits^{f \in L_{p,p}^l (G^n )} } \frac{{\left\| {D^\alpha f} \right\|_{L_p (G^n )} }}{{\left\| f \ri...