Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis
- A. A. Vasil’eva
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A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L p space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted L p -space.
- É. N. Batuev and V.D. Stepanov, “Weighted Inequalities of Hardy Type,” Sibirsk. Mat. Zh. 30(1), 13–22 (1989) [Siberian Math. J. 30 (1), 8–16 (1989)].
- V. D. Stepanov, “Two-Weight Estimates for Riemann-Liouville Integrals,” Izv. Akad. Nauk SSSR Ser. Mat. 54(3), 645–655 (1990) [Math.-USSR-Izv. 36 (3), 669–681 (1991)].
- V. D. Stepanov, “Two-Weighted Estimates for Riemann-Liouville Integrals,” Rept. 39, Ceskoslov. Akad. Věd. Mat. Ústav. (Praha, 1988).
- V. D. Stepanov, “Weighted Norm Inequalities for Integral Operators and Related Topics,” in Nonlinear Analysis, Function Spaces and Applications, Proceedings of the Spring School Held in Prague, May 23–28, 1994, Vol. 5, Ed. by M. Krbec, A. Kufner, B. Opic, and J. Rakosnik (Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha, 1995), pp. 139–175.
- V. D. Stepanov, “Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators,” J. London Math. Soc. 50(1), 105–120 (1994).
- N. P. Korneichuk, Splines in Approximation Theory (Nauka, Moscow, 1984) [in Russian].
- G. G. Lorentz, Approximation of Functions (Hdt Rinehart, Winston, New York, 1966).
- A. Pinkus, n-Widths in Approximation Theory (Springer, Berlin: 1985).
- V. M. Tikhomirov, Some Questions in Approximation Theory (Izdat. Moskov. Univ., Moscow, 1976).
- V. M. Tikhomirov, “Approximation Theory,” in Current Problems in Mathematics. Fundamental Directions 14 (Itogi Nauki i Tekhniki) (Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987), pp. 103–260.
- Yu. [Ju.] I. Makovoz, “A Certain Method of Obtaining Lower Estimates for Diameters of Sets in Banach Spaces,” Mat. Sb. 87(129) (1), 136–142 (1972).
- Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis
Russian Journal of Mathematical Physics
Volume 16, Issue 4 , pp 543-562
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- Print ISSN
- Online ISSN
- SP MAIK Nauka/Interperiodica
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- A. A. Vasil’eva (1)
- Author Affiliations
- 1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia