Inequalities for upper bounds of functionals on the classes $W^r H^{ω}$ and their applications

• Datum: 2000
• Hauptverfasser: Babenko, V. F., Korneichuk, N. P., Kofanov, V. A., Pichugov, S. A., Бабенко, В. Ф., Корнейчук, Н. П., Кофанов, В. А., Пичугов, С. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2000
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4398
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We show that the well-known results on estimates of upper bounds of functionals on the classes $W^r H^{ω}$ of periodic functions can be regarded as a special case of Kolmogorov-type inequalities for support functions of convex sets. This enables us to prove numerous new statements concerning the app...