Moduli of continuity defined by zero continuation of functions and K-functionals with restrictions

• Date: 1996
• Main Authors: Radzievskii, G. V., Радзиевский, Г. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5208
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the followingK-functional: $$K(\delta ,f)_p : = \mathop {\sup }\limits_{g \in W_{p U}^r } \left\{ {\left\| {f - g} \right\|_{L_p } + \delta \sum\limits_{j = 0}^r {\left\| {g^{(j)} } \right\|_{L_p } } } \right\}, \delta \geqslant 0,$$ where ƒ ∈L p :=L p [0, 1] andW p,U r is a s...