Estimates for Hardy-type integral operators in weighted Lebesgue spaces

• Main Author: Arendarenko, Larissa
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: Luleå tekniska universitet, Matematiska vetenskaper 2013
• Subjects: Mathematical Analysis; Matematisk analys; Luleå
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25949

This PhD thesis deals with the theory of Hardy-type inequalities in a new situation, namely when the classical Hardy operator is replaced by a more general operator with a kernel. The kernels we consider belong to the new classes $\mathcal{O}^+_n$ and $\mathcal{O}^-_n$, $n=0,1,.$, which are wider than co-called Oinarov class of kernels. This PhD thesis consists of four papers (papers A, B, C and D), two complementary appendixes (A$_1$, C$_1$) and an introduction, which put these publications into a more general frame. This introduction also serves as a basic overview of the field. In paper A some boundedness criteria for the Hardy-Volterra integral operators are proved and discussed. The case $1<q Godkänd; 2013; 20130426 (larare); Tillkännagivande disputation 2013-05-08 Nedanstående person kommer att disputera för avläggande av teknologie doktorsexamen. Namn: Larissa Arendarenko Ämne: Matematik/Mathematics Avhandling: Estimates for Hardy-type Integral Operators in Weighted Lebesgue Spaces Opponent: Professor Massimo Lanza de Cristoforis, Dipartamento di Matematica Universita degli Studi di Padova, Padova, Italy, Ordförande: Professor Peter Wall, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Tid: Måndag den 3 juni 2013, kl 10.00 Plats: E246, Luleå tekniska universitet