Geodesic
On a Kudryavtsev type function space
Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 34-46.

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In the paper we introduce a Kudryavtsev type space, the norm of which contains a differential operator called the multiweighted derivative. This type of spaces has been studied in details for power weights. Here we consider general weights. The main result of the paper is the proof of the existence of a generalized polynomial, to which functions of this space stabilize at a singular point, so that the coefficients of this polynomial can be considered as the characteristics of the behaviour of a function nearby this singularity. 
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A. A. Kalybay; Zh. A. Keulimzhayeva; R. Oinarov. On a Kudryavtsev type function space. Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 34-46. http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a4/

[1] Z. T. Abdikalikova, Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives, PhD Thesis, Lule a University of Technology, 2009

[2] B. L. Baideldinov, Theory of multiweighted spaces and its application to boundary problems for singular differential equations, Doctoral Thesis, Almaty, 1998 (in Russian)

[3] A. A. Kalybay, A new development of Nikol'skii-Lizorkin and Hardy type inequalities with applications, PhD Thesis, Lule a University of Technology, 2006

[4] L. D. Kudryavtsev, Selected Works, Chapter I, v. II, Function spaces. Differential equations, Fizmatlit, M., 2008 (in Russian)

[5] L. D. Kudryavtsev, Selected Works, Chapter II, v. II, Function spaces. Differential equations, Fizmatlit, M., 2008 (in Russian)

[6] L. D. Kudryavtsev, “On norms in weighted spaces of functions given on infinite intervals”, Anal. Math., 12:4 (1986), 269–282 | DOI | MR | Zbl

[7] R. Oinarov, “Boundedness and compactness of Volterra type integral operators”, Siberian Math. J., 48:5 (2007), 884–896 | DOI | MR | Zbl