Sobolev spaces "with mixed functions"

• Autorzy: Liskowski M.
• Języki publikacji: EN

Abstrakty

EN

This paper describes some generalization of modular function spaces L_ϕψ defined by a modular I_ϕѱ(f) = ∫^b_aϕ (x, ∫^d_c ψ (y, f (x,y))dy) dx, ([3]). The next part of this paper focuses on using of spaces, defined previously, to introduce Sobolev spaces as a vector subspace of the generalized space L_ϕѱ. Some selected properties of these spaces are presented.

Słowa kluczowe

EN

modular space; Sobolev space

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2012
• Tom: Nr 48
• Strony: 73--82
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Liskowski M.

• Institute of Mathematics Poznan University of Technology Piotrowo 3A, 60-965 Poznan

Bibliografia

• [1] Adams R.A., Sobolev spaces, Academic Press, New York, ”San Francisco” London, 1975.
• [2] Liskowski M., On approximation by means of linear operators in generalized Orlicz spaces, Int. Journal of Pure and Applied Mathematics, 37(2)(2007), 165-180.
• [3] Musielak J., On approximation of functions of two variables by integral means and their generalization, Atti Sem. Mat. Univ. Modena, XLVI (1998), 335-349.