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Some new boundedness and compactness results for discrete Hardy type operators with kernels
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction and three papers, which deal with some new discrete Hardy type inequalities. In the introduction we give an overview of the area that serves as a frame for the rest of the thesis. In particular, a short description of the development of Hardy type inequalities is given.In Paper 1 we prove a new discrete Hardy-type inequality $$ \|Af\|_{q,u}\leq C\|f\|_{p,v},~~~~1$$where the matrix operator $A$ is defined by $\left(Af\right)_i:=\sum\limits_{j=1}^ia_{i,j}f_j,$ ~$a_{i, j}\geq 0$, where the entries $a_{i, j}$ satisfies less restrictive additional conditions than studied before. Moreover, we study the problem of compactness for the operator $A$, and also the dual result is stated, proved and discussed.In Paper 2 we derive the necessary and sufficient conditions for inequality (1) to hold for the case $1 In Paper 3 we consider an operator of multiple summation with weights in weighted sequence spaces, which cover a wide class of matrix operators and we state, prove and discuss both boundedness and compactness forthis operator, for the case $1

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2009. , 6 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
Research subject
URN: urn:nbn:se:ltu:diva-16858Local ID: 04d28ad0-2ffa-11de-bd0f-000ea68e967bISBN: 978-91-86233-39-6OAI: diva2:989845
Godkänd; 2009; 20090423 (aintem); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Torsdag den 4 juni 2009 kl 13.00 Plats: D 2214, Luleå tekniska universitetAvailable from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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