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The results presented in this paper concern the identity of spaces Wk, M Ω and Wk, M Ω generated by &phi-functions M with parameter for some class domains Ω ⊂ Rn and they are the extension of analogous results for clasical Sobolev spaces. The problem of approximation of elements in Wk, M Ω by smooth functions on various domains Ω ⊂ Rn were investigated by different authors for classic Sobolev spaces with integer values of k as well as for some generalization of Sobolev space to the case of noninteger values k (see e.g. N. Meyers and J. Serrin [11] in the case M(u) =up, p> 1; T. K. Donaldson and N. S. Trudinger [2], when M is arbitrary N-function; H. Hudzik [3], [4], [5], [6]. [7], when M is TV-function which depends on parameter; M. Liskowski [9] [10] for some family of generalized Orlicz-Sobolev space, when k is noninteger and M is N-function with parameter).
Czasopismo
Rocznik
Tom
Strony
73-82
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Institute of Mathematics, Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland, mliskows@math.put.poznan.pl
Bibliografia
- [1] Adams R.A., Sobolev spaces, Academic Press, New York - San Francisco -London 1975.
- [2] Donaldson T.K., Trudinger N.S., Orlicz-Sobolev spaces and imbedding theorems, J. Functional Analysis, 8(1971), 52-75.
- [3] Hudzik H., On density of C0∞(Ω) in Orlicz-Sobolev space WkM(Ω) for every open set Ω c Rn , Funct, et Approximatio, 5(1977), 113-128.
- [4] Hudzik H., On problem of density of in generalized Orlicz-Sobolev space WkM(Ω) for every open set Ω c Rn , Comm. Mathematicae, 20(1977), 5-78.
- [5] Hudzik H., On continuity of the imbedding operation from WkM(Ω) into WkM2(Ω), Funct, et Approximatio, 6(1978), 111-118.
- [6] Hudzik H., Density of C0∞(Ω) in generalized Orlicz-Sobolev space WkM(Ω), Funct. et Approximatio, 7(1979), 15-21.
- [7] Hudzik H., The problems of separability, duality, reflexivity and of comparison for generalized Orlicz-Sobolev spaces WkM(Ω), Comm. Mathematicae, 21(1979), 315-324.
- [8] Kozek A. Convex integral functionals in Orlicz spaces. Comm. Mathematicae, 21(1979), 109-135.
- [9] Liskowski M., Density of C0∞(Rn) generalized Besov space Bk,ɸ(Rn) Funct. et Approximatio, 15(1986), 185-193.
- [10] Liskowski M., Approximation in Orlicz-Slobodecki space by functions in C∞(Ω), Fasciculi Mathematici, 29(1999), 43-54.
- [11] Meyers N., Serrin J., H = W, Proc. Nat. Acad. Sci., USA, 51(1964), 1055-1056.
- [12] Musielak J., Orlicz spaces and modular spaces. Lecture Notes in Math. 1034, Springer, 1983.
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Bibliografia
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bwmeta1.element.baztech-article-BPP1-0059-0045