Abstract
Let l ∈ ℕ, A ⊂ ℝn . The main goal of this paper is to describe (in inner terms) the closure of the set {f ∈ W l1 : f=0 in a neighborhood of the set A} with respect to the norm of the space W l1 (ℝn). Bibliography: 9 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
L. I. Hedberg, “Two approximation problems in function spaces,”Ark. Mat.,16, 51–81 (1987).
L. I. Hedberg and T. H. Wolff, “Thin sets in non-linear potential theory,”Ann. Inst. Fourier,33, 161–187 (1983).
L. I. Hedberg, “Spectral synthesis in Sobolev spaces,” in:Linear and Complex Analysis Problem Book, Lect. Notes Math.,1043, 435–437 (1984).
Yu. V. Netrusov, “Spectral synthesis in spaces of smooth functions”Dokl. Ros. Akad. Nauk. 325, 923–925 (1992).
T. Bagby and W. P. Ziemer, “Pointwise differentiability and absolute continuity,”Trans. Amer. Math. Soc.,191, 129–148 (1974).
L. Carleson,Selected Problems in the Theory of Exceptional Sets (1971).
V. G. Maz'ya,S. L. Sobolev Spaces [in Russian], Leningrad (1985).
O. V. Besov, V. P.Il'in, and S. M. Nikolskii,Integral Representations of Functions and Embedding Theorems [in Russian], Moscow (1975).
V. G. Maz'ya and T. O Shaposhnikova,Multipliers in Spaces of Differentiable Functions [in Russian], Leningrad (1986).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 92–111.
Rights and permissions
About this article
Cite this article
Netrusov, Y.V. Spectral synthesis in the sobolev space generated by an integral metric. J Math Sci 85, 1814–1826 (1997). https://doi.org/10.1007/BF02355292
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02355292