Some new boundedness and compactness results for discrete Hardy type operators with kernels
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...
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Luleå tekniska universitet, Matematiska vetenskaper
2009
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ftluleatu:oai:DiVA.org:ltu-16858 2023-05-15T17:09:06+02:00 Some new boundedness and compactness results for discrete Hardy type operators with kernels Temirkhanova, Ainur 2009 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16858 eng eng Luleå tekniska universitet, Matematiska vetenskaper Luleå Licentiate thesis / Luleå University of Technology, 1402-1757 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16858 urn:isbn:978-91-86233-39-6 Local 04d28ad0-2ffa-11de-bd0f-000ea68e967b info:eu-repo/semantics/openAccess Mathematical Analysis Matematisk analys Licentiate thesis, comprehensive summary info:eu-repo/semantics/masterThesis text 2009 ftluleatu 2022-10-25T20:50:45Z 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 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 universitet Master Thesis Luleå Luleå Luleå University of Technology Publications (DiVA) Persson ENVELOPE(-58.400,-58.400,-64.200,-64.200) |
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Open Polar |
collection |
Luleå University of Technology Publications (DiVA) |
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ftluleatu |
language |
English |
topic |
Mathematical Analysis Matematisk analys |
spellingShingle |
Mathematical Analysis Matematisk analys Temirkhanova, Ainur Some new boundedness and compactness results for discrete Hardy type operators with kernels |
topic_facet |
Mathematical Analysis Matematisk analys |
description |
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 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 universitet |
format |
Master Thesis |
author |
Temirkhanova, Ainur |
author_facet |
Temirkhanova, Ainur |
author_sort |
Temirkhanova, Ainur |
title |
Some new boundedness and compactness results for discrete Hardy type operators with kernels |
title_short |
Some new boundedness and compactness results for discrete Hardy type operators with kernels |
title_full |
Some new boundedness and compactness results for discrete Hardy type operators with kernels |
title_fullStr |
Some new boundedness and compactness results for discrete Hardy type operators with kernels |
title_full_unstemmed |
Some new boundedness and compactness results for discrete Hardy type operators with kernels |
title_sort |
some new boundedness and compactness results for discrete hardy type operators with kernels |
publisher |
Luleå tekniska universitet, Matematiska vetenskaper |
publishDate |
2009 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16858 |
long_lat |
ENVELOPE(-58.400,-58.400,-64.200,-64.200) |
geographic |
Persson |
geographic_facet |
Persson |
genre |
Luleå Luleå |
genre_facet |
Luleå Luleå |
op_relation |
Licentiate thesis / Luleå University of Technology, 1402-1757 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16858 urn:isbn:978-91-86233-39-6 Local 04d28ad0-2ffa-11de-bd0f-000ea68e967b |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1766065032825667584 |