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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].

##### MSC:
 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 26D10 Inequalities involving derivatives and differential and integral operators
##### Keywords:
Hardy inequality of order $$k$$