Concave shells of continuity modules

• Date: 2019
• Main Authors: Pichugov, S. A., Пичугов, С. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1470
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 The inequality $$ \overline{\omega}(t)\leq\inf_{s>0}\left(\omega\left(\dfrac{s}{2}\right)+\dfrac{\omega(s)}{s}t\right) $$ is proved, where $\omega(t)$ is a function of the modulus of continuity type and $\overline{\omega}(t)$ is its smallest concave majorant. The consequences...