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  • 1.
    Abdikalikova, Zamira
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Compactness of embedding between Sobolev type spaces with multiweighted derivatives2009In: 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.

  • 2.
    Abdikalikova, Zamira
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Embedding theorems for spaces with multiweighted derivatives2007Licentiate 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.

  • 3.
    Abdikalikova, Zamira
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives2009Doctoral 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.

  • 4. Abdikalikova, Zamira
    et al.
    Baiarystanov, Askar O.
    Oinarov, Ryskul
    Compactness of embedding between spaces with multiweighted derivatives: the case 1 ≤ p ≤ q2009Report (Other academic)
  • 5.
    Abdikalikova, Zamira
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Kalybay, Aigerim
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Summability of a Tchebysheff system of functions2007Report (Other academic)
1 - 5 of 5
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