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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 2, 1997, pp. 387–403
DOI: 10.4171/ZAA/769

Published online: 1997-06-30

Hardy Inequalities for Overdetermined Classes of Functions

Alois Kufner[1] and C.G. Simader[2]

(1) University of West Bohemia, Plzen, Czech Republic
(2) Universität Bayreuth, Germany

Conditions on weights $w_0$ and $w_k$ are given for the $k$-th order Hardy inequality $(\int^1_0 |u(t)|^q w_0(t)dt^{1/q} ≤ c(\int^1_0 |u^{(k)}(t)|^p w_k(t) dt)^{1/p}$ to hold for two special classes of functions $u$ satisfying $2k$ and $k + 1$ boundary conditions, respectively. The conditions are sufficient and partially also necessary. For one class, a hypothesis is formulated describing necessary and sufficient conditions on $w_0$ and $w_k$.

Keywords: Hardy’s inequality, weighted norm inequalities

Kufner Alois, Simader C.G.: Hardy Inequalities for Overdetermined Classes of Functions. Z. Anal. Anwend. 16 (1997), 387-403. doi: 10.4171/ZAA/769