JournalszaaVol. 16, No. 2pp. 387–403

Hardy Inequalities for Overdetermined Classes of Functions

  • Alois Kufner

    University of West Bohemia, Plzen, Czech Republic
  • C.G. Simader

    Universität Bayreuth, Germany
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Abstract

Conditions on weights w0w_0 and wkw_k are given for the kk-th order Hardy inequality (01u(t)qw0(t)dt1/qc(01u(k)(t)pwk(t)dt)1/p(\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 uu satisfying 2k2k and k+1k + 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 w0w_0 and wkw_k.

Cite this article

Alois Kufner, C.G. Simader, Hardy Inequalities for Overdetermined Classes of Functions. Z. Anal. Anwend. 16 (1997), no. 2, pp. 387–403

DOI 10.4171/ZAA/769