Brown, Richard; Hinton, Don Interpolation inequalities with power weights for functions of one variable. (English) Zbl 0779.26012 J. Math. Anal. Appl. 172, No. 1, 233-242 (1993). The aim of the paper is to find simple, sufficient conditions for the validity of an interpolation inequality of the form \[ \left(\int_ I| x^ \beta u^{(j)}|^ pdx\right)^{1/p}\leq K\left(\int_ I| x^ \gamma u|^ qdx\right)^{(1-\lambda)/q}\left(\int_ I| x^ \alpha u^{(n)}|^ rdx\right)^{\lambda/r}, \tag{1} \] where \(1\leq p,q,r\leq\infty\), \(0\leq j\leq n-1\), \(I\) is one of the intervals \((0,\infty)\), \((0,b]\) or \([b,\infty)\) with \(b>0\), and the function \(u\) is in an appropriate subspace of \(AC^{(n)}(I)\). The method used to prove the inequality (1) is elegant and it is based on some results on Hardy- type inequalities and the Gabushin inequality. Reviewer: B.Opic (Praha) Cited in 2 Documents MSC: 26D15 Inequalities for sums, series and integrals 26D10 Inequalities involving derivatives and differential and integral operators Keywords:interpolation inequality; Hardy-type inequalities; Gabushin inequality PDFBibTeX XMLCite \textit{R. Brown} and \textit{D. Hinton}, J. Math. Anal. Appl. 172, No. 1, 233--242 (1993; Zbl 0779.26012) Full Text: DOI