Inequalities for derivatives of functions on an axis with nonsymmetrically bounded higher derivatives

• Date: 2012
• Main Authors: Kofanov, V. A., Кофанов, В. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2604
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For nonperiodic functions $x \in L^r_{\infty}(\textbf{R})$ defined on the entire real axis, we prove analogs of the Babenko inequality. The obtained inequalities estimate the norms of derivatives $||x^{(k)}_{\pm}||_{L_q[a, b]}$ on an arbitrary interval $[a,b] \subset R$ such that $x^{(k)}(a) = x^{(...