2017
Том 69
№ 9

All Issues

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

Kofanov V. A.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 5, pp 721-736.

Citation Example: Kofanov V. A. Inequalities for derivatives of functions on an axis with nonsymmetrically bounded higher derivatives // Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 636-648.

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