TY - JOUR
AU - V. A. Kofanov
PY - 2012/05/25
Y2 - 2024/06/24
TI - Inequalities for derivatives of functions on an axis with nonsymmetrically bounded higher derivatives
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 64
IS - 5
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2604
AB - 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.
ER -