01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
03.05.1948
E-mail:
, ,
Keywords:
embeddings of the functional spaces; interpolation spaces; maximal functions and singular operators; theory of approximation.
Subject:
Embeddings and interpolation of functional spaces; maximal and singular operators and weighted inequalities; best approximation in functional spaces. The embedding problems of general weighted Sobolev spaces in isotrophic and anisotrophic cases were solved; interpolation spaces of general weighted Sobolev classes were described.
Biography
Graduated from Mathematics and Mechanics Faculty of Novosibirsk State University — 1972. Ph.D — 1981. D.Sci — 2000. Since 1997 I am working as head of researches financed by grants (1997–999, 2000–2002). The subject of researches is Qualitative and structural characteristics of differentiable functions and differential operators.
Main publications:
Kusainova L. K. Ob interpolyatsii vesovykh prostranstv Soboleva // Izvestiya Ministerstva nauki Akademii nauk Respubliki Kazakhstan, 1997, seriya fiziko-matematicheskaya 5 (198). C. 33–51.
Kusainova L. K. Vesovye neravenstva vlozhenii // Doklady Ministerstva nauki Akademii nauk Respubliki Kazakhstan, 1998, # 6. C. 23–32.
Kusainova L. K. O vlozhenii vesovogo prostranstva Soboleva $W^l_p(\Omega;v)$ v prostranstva Lebega $L_p(\Omega;\omega)$ // Matematicheskii sbornik, 2000, 191 (2). C. 132–148.
A. Kasym, L. K. Kusainova, “On the separation property of the Sturm–Liouville operator in weighted spaces of multiplicators”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 141 (2017), 86–94; Journal of Mathematical Sciences, 241:5 (2019), 596–604
2.
L. K. Kusainova, B. S. Koshkarova, “Oscillatory and nonoscillatory conditions for a second-order half-linear differential equation”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139 (2017), 39–43; Journal of Mathematical Sciences, 241:3 (2019), 285–289
2016
3.
L. K. Kusainova, A. Myrzagaliyeva, Ya. T. Sultanaev, “On the Boundedness of the Schrödinger Operator in Weighted Sobolev Spaces”, Mat. Zametki, 99:6 (2016), 945–949; Math. Notes, 99:6 (2016), 948–953
L. K. Kusainova, A. Zh. Monashova, A. A. Shkalikov, “Asymptotics of Eigenvalues of a Second-Order Non-Self-Adjoint Differential Operator on the Axis”, Mat. Zametki, 93:4 (2013), 630–633; Math. Notes, 93:4 (2013), 629–632
L. K. Kusainova, “Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the space $L_p(\Omega;\omega)$”, Mat. Sb., 191:2 (2000), 132–148; Sb. Math., 191:2 (2000), 275–290
L. K. Kusainova, “Embedding theorems for anisotropic [weighted] spaces of Sobolev type. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 11, 20–31; Soviet Math. (Iz. VUZ), 31:11 (1987), 27–39
1982
10.
L. K. Kusainova, K. T. Mynbaev, “On imbedding and compactness theorems for anisotropic weighted Sobolev spaces”, Dokl. Akad. Nauk SSSR, 263:5 (1982), 1050–1053
1980
11.
L. K. Kusainova, “Estimates of diameters of the unit sphere of the function space $\mathring{L}^l_p(\Omega,v)$ in $L_q(\Omega)$”, Dokl. Akad. Nauk SSSR, 251:4 (1980), 791–794
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