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Some remarks concerning the Hardy inequality. (English) Zbl 0794.46021
Schmeisser, Hans-Jürgen (ed.) et al., Function spaces, differential operators and nonlinear analysis. Survey articles and communications of the international conference held in Friedrichsroda, Germany, September 20-26, 1992. Stuttgart: B. G. Teubner Verlagsgesellschaft. Teubner-Texte Math. 133, 290-294 (1993).
Summary: This note deals with the Hardy inequality of order \(k\) \[ \left(\int^ \infty_ 0 | u(t)|^ q w_ 0(t)dt\right)^{1/q}\leq C\left(\int^ \infty_ 0 | u^{(k)}(t)|^ p w_ k(t)dt\right)^{1/p},\tag{1} \] more precisely, with conditions on the parameters \(p\), \(q\) and on the weight functions \(w_ 0\), \(w_ k\) under which inequality (1) holds for all functions \(u\) from a certain class \(K\) with a constant \(C>0\) independent of \(u\).
For the entire collection see [Zbl 0782.00088].

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators