CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt170",{id:"formSmash:upper:j_idt170",widgetVar:"widget_formSmash_upper_j_idt170",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt178_j_idt181",{id:"formSmash:upper:j_idt178:j_idt181",widgetVar:"widget_formSmash_upper_j_idt178_j_idt181",target:"formSmash:upper:j_idt178:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Estimates for Hardy-type integral operators in weighted Lebesgue spacesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2013. , p. 138
##### Series

Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:ltu:diva-25949Local ID: bd49fa45-29fb-40bc-b910-dc8b1f3bbcb3ISBN: 978-91-7439-614-0 (print)ISBN: 978-91-7439-615-7 (electronic)OAI: oai:DiVA.org:ltu-25949DiVA, id: diva2:999107
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt825",{id:"formSmash:j_idt825",widgetVar:"widget_formSmash_j_idt825",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt837",{id:"formSmash:j_idt837",widgetVar:"widget_formSmash_j_idt837",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt852",{id:"formSmash:j_idt852",widgetVar:"widget_formSmash_j_idt852",multiple:true});
##### Note

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 $1<q<p<\infty$ is considered and the involved kernels are from the classes $\mathcal{O}^+_1$ and $\mathcal{O}^-_1$. A complete solution of the problem is presented and discussed. The appendix to paper A contains the proof of Theorem 3.1, which is not included in the paper. In paper B even more complicated (than in paper A) case with variable limits on the Hardy operator is investigated. The main results of the paper are proved by applying the block-diagonal method given by Batuev and Stepanov and the results from paper A. Paper C deals with Hardy-type inequalities restricted to the cones of monotone functions. The case $1<p\le q<\infty$ is considered and the involved kernels satisfy conditions, which are less restrictive than the usual Oinarov condition. Also in this case a complete solution is obtained and some concrete applications are pointed out. In particular, in paper C some open questions are raised. These questions are discussed and solved in an appendix to Paper C. In paper D we study superpositions of the Hardy-Volterra integral operator and its adjoint. The boundedness and compactness criteria in the range of parameters $1<p\le q<\infty$ are obtained and discussed. Moreover, some new properties of the classes $\mathcal{O}^+_n$ and $\mathcal{O}^-_n$ are proved.

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

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-02-14Bibliographically approved
isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1878",{id:"formSmash:j_idt1878",widgetVar:"widget_formSmash_j_idt1878",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1931",{id:"formSmash:lower:j_idt1931",widgetVar:"widget_formSmash_lower_j_idt1931",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1932_j_idt1934",{id:"formSmash:lower:j_idt1932:j_idt1934",widgetVar:"widget_formSmash_lower_j_idt1932_j_idt1934",target:"formSmash:lower:j_idt1932:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});