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

  • V. A. Kofanov


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 $x^{(k)}(a) = x^{(k)}(b) = 0$ via local $L_p$-norms of the functions $x$ and uniform nonsymmetric norms of the higher derivatives $x(r)$ of these functions.
How to Cite
Kofanov, V. A. “Inequalities for Derivatives of Functions on an Axis With Nonsymmetrically Bounded Higher Derivatives”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 5, May 2012, pp. 636-48,
Research articles