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This article is cited in 3 scientific papers (total in 3 papers)
Inequalities between derivatives in $L_p$-metrics for $0<p\leqslant\infty$
V. N. Gabushin
Abstract:
We consider inequalities of the form
\begin{equation}
\|f^{(k)}\|_{L_q}\leqslant K\|f\|^\alpha_{L_p}\|\Phi\|^\beta_{L_r},
\tag{1}
\end{equation}
where $\Phi(x)$ is an arbitrary majorant of the function $f^{(l)}(x)$, $x\in(-\infty,\infty)$, $k\leqslant l$. The set of parameters $p,q,r,k,l$ for which the inequalities (1) hold is described. Various generalizations of these inequalities are given.
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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:4, 823–844
Bibliographic databases:
 
UDC:
517.5
MSC: Primary 26A86, 26A84, 46E30; Secondary 46E35
Received: 15.07.1974
Citation:
V. N. Gabushin, “Inequalities between derivatives in $L_p$-metrics for $0<p\leqslant\infty$”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976), 869–892; Math. USSR-Izv., 10:4 (1976), 823–844
Citation in format AMSBIB
\Bibitem{Gab76}
\by V.~N.~Gabushin
\paper Inequalities between derivatives in $L_p$-metrics for $0<p\leqslant\infty$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 4
\pages 869--892
\mathnet{http://mi.mathnet.ru/izv2208}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=430772}
\zmath{https://zbmath.org/?q=an:0332.46017}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 4
\pages 823--844
\crossref{https://doi.org/10.1070/IM1976v010n04ABEH001817}
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V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126
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A. I. Zvyagintsev, “Strict inequalities for the derivatives of functions satisfying certain boundary conditions”, Math. Notes, 62:5 (1997), 596–606
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A. V. Gasnikov, “Time-asymptotic behaviour of a solution of the Cauchy initial-value problem for a conservation law with non-linear divergent viscosity”, Izv. Math., 73:6 (2009), 1111–1148
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