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Abdikalikova, Zamira
Publications (5 of 5) Show all publications
Abdikalikova, Z. (2009). Compactness of embedding between Sobolev type spaces with multiweighted derivatives (ed.). In: (Ed.), AIHT : Analysis, Inequalities and Homogenization Theory: Midnight sun conference in honor of Lars-Erik Persson. Paper presented at Analysis, Inequalities and Homogenization Theory : 08/06/2009 - 11/06/2009.
Open this publication in new window or tab >>Compactness of embedding between Sobolev type spaces with multiweighted derivatives
2009 (English)In: AIHT : Analysis, Inequalities and Homogenization Theory: Midnight sun conference in honor of Lars-Erik Persson, 2009Conference paper (Other academic)
Abstract [en]

We consider a new Sobolev type function space called the space with multiweighted derivatives. As basis for this space serves some differential operators containing weight functions. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding between the spaces with multiweighted derivatives in different selections of weights.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-34781 (URN)911d8150-5725-11de-9f57-000ea68e967b (Local ID)911d8150-5725-11de-9f57-000ea68e967b (Archive number)911d8150-5725-11de-9f57-000ea68e967b (OAI)
Conference
Analysis, Inequalities and Homogenization Theory : 08/06/2009 - 11/06/2009
Note

Godkänd; 2009; 20090612 (evan)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-02-27Bibliographically approved
Abdikalikova, Z., Baiarystanov, A. O. & Oinarov, R. (2009). Compactness of embedding between spaces with multiweighted derivatives: the case 1 ≤ p ≤ q (ed.). Paper presented at . Luleå: Department of Mathematics, Luleå University of Technology
Open this publication in new window or tab >>Compactness of embedding between spaces with multiweighted derivatives: the case 1 ≤ p ≤ q
2009 (English)Report (Other academic)
Place, publisher, year, edition, pages
Luleå: Department of Mathematics, Luleå University of Technology, 2009. p. 22
Series
Gula serien, ISSN 1400-4003 ; 2009:06
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-21790 (URN)02466b2c-a6f6-40f5-aa79-1a37b50f412c (Local ID)02466b2c-a6f6-40f5-aa79-1a37b50f412c (Archive number)02466b2c-a6f6-40f5-aa79-1a37b50f412c (OAI)
Note
Godkänd; 2009; 20120319 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Abdikalikova, Z. (2009). Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives (ed.). (Doctoral dissertation). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions.Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we prove some new estimates for each function in a Tchebychev system. In order to be able to study compactness of the embeddings from Chapter 3 such estimates are crucial.In Chapter 3 we rewrite and present some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we rewrite and discuss some analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are not available in the Western literatures in this way and they are crucial for the proofs of the main results in Chapter 4. In Chapter 4 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of the spaces. However, with the help of our new embedding theorems we can extend theseresults to the case of strong degeneration.The main aim of Chapter 5 is to establish boundedness and compactness of the embedding considered in Chapter 4.In Chapter 4 basically only sufficient conditions for boundedness of this embedding were obtained. In Chapter 5 we obtain necessary and sufficient conditions for boundedness and compactness of this embedding and the main results are proved in a different way.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2009. p. 100
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-25800 (URN)b2e28090-349a-11de-98cd-000ea68e967b (Local ID)978-91-86233-43-3 (ISBN)b2e28090-349a-11de-98cd-000ea68e967b (Archive number)b2e28090-349a-11de-98cd-000ea68e967b (OAI)
Note

Godkänd; 2009; 20090429 (zamira); DISPUTATION Ämnesområde: Matematik/Mathematics Opponent: Professor Victor Burenkov, Cardiff University, United Kingdom Ordförande: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Fredag den 12 juni 2009, kl 10.00 Plats: D 2214, Luleå tekniska universitet

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-02-27Bibliographically approved
Abdikalikova, Z. (2007). Embedding theorems for spaces with multiweighted derivatives (ed.). (Licentiate dissertation). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Embedding theorems for spaces with multiweighted derivatives
2007 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate Thesis consists of four chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we consider and analyze some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we present and prove analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are crucially for the proofs of the main results of this Licentiate Thesis. In Chapter 3 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of spaces. However, with the help of our new embedding theorems we can extend these results to the case of strong degeneration. In Chapter 4 we prove some new estimates for each function in a Tchebychev system. In order to be able to study also compactness of the embeddings from Chapter 3 such estimates are crucial. I plan to study this question in detail in my further PhD studies.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2007. p. 84
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2007:53
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-26092 (URN)c9a3e4e0-8d25-11dc-a188-000ea68e967b (Local ID)c9a3e4e0-8d25-11dc-a188-000ea68e967b (Archive number)c9a3e4e0-8d25-11dc-a188-000ea68e967b (OAI)
Note

Godkänd; 2007; 20071107 (ysko)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-02-27Bibliographically approved
Abdikalikova, Z. & Kalybay, A. (2007). Summability of a Tchebysheff system of functions (ed.). Paper presented at . Luleå: Department of Mathematics, Luleå University of Technology
Open this publication in new window or tab >>Summability of a Tchebysheff system of functions
2007 (English)Report (Other academic)
Place, publisher, year, edition, pages
Luleå: Department of Mathematics, Luleå University of Technology, 2007. p. 17
Series
Gula serien, ISSN 1400-4003 ; 2007:05
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-24987 (URN)d52ccddc-f0a7-494e-9793-1d49c3b70365 (Local ID)d52ccddc-f0a7-494e-9793-1d49c3b70365 (Archive number)d52ccddc-f0a7-494e-9793-1d49c3b70365 (OAI)
Note

Godkänd; 2007; 20120507 (andbra)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-27Bibliographically approved

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