Inequalities for derivatives of functions on an axis with nonsymmetrically bounded higher derivatives - Kofanov, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
For nonperiodic functions $x \in L^r_{∞}(R)$ defined on the entire real axis, we prove analogs of the Babenko inequality. The obtained inequalities estimate the norms of derivatives $||x^{(k)}_{±}||_{L_q[a, b]}$ 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.