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 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] 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.