Strengthening of the Kolmogorov Comparison Theorem and Kolmogorov Inequality and Their Applications

• Datum: 2002
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2002
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4173
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We obtain a strengthened version of the Kolmogorov comparison theorem. In particular, this enables us to obtain a strengthened Kolmogorov inequality for functions x ∈ L ∞ x (r), namely, $$\left\| {x^{(k)} } \right\|_{L_\infty (R)} \leqslant \frac{{\left\| {\phi _{r - k} } \right\|_\infty }}{{\l...