Some new Hardy-type Inequalities for integral operators with kernels

This Licentiate thesis deals with the theory of Hardy-type inequalities in anew situation, namely when the classical Hardy operator is replaced by amore general operator with kernel. The kernels we consider belong to thenew classes O+ n and O-n , n = 0; 1; :::, which are wider than co-called Oinarovclass of kernels.The thesis consists of three papers (papers A, B and C), an appendix topaper A and an introduction, which gives an overview to this specific fieldof functional analysis and also serves to put the papers in this thesis into amore general frame.In paper A some new Hardy-type inequalities for the case with Hardy-Volterra integral operators involved are proved and discussed. The case 1<p>Godkänd; 2011; 20111114 (larare); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Professor Massimo Lanza de Cristoforis, Dipartamento di Matematica, Universita degli Studi di Padova, Italy Tid: Tisdag den 20 december 2011 kl 10.00 Plats: D2214-15, Luleå tekniska universitet