Geodesic
Some approximation results in Musielak-Orlicz spaces
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 453-471
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We prove the continuity in norm of the translation operator in the Musielak-Orlicz $L_{M}$ spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in $L_{M}$, in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.
We prove the continuity in norm of the translation operator in the Musielak-Orlicz $L_{M}$ spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in $L_{M}$, in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.
DOI : 10.21136/CMJ.2019.0355-18
Classification : 46B10, 46E30
Keywords: approximate identity; Musielak-Orlicz space; density of smooth functions 
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Youssfi, Ahmed; Ahmida, Youssef. Some approximation results in Musielak-Orlicz spaces. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 453-471. doi: 10.21136/CMJ.2019.0355-18

[1] Adams, R. A., Fournier, J. J. F.: Sobolev Spaces. Pure and Applied Mathematics 140, Academic Press, New York (2003). | DOI | MR | JFM

[2] Benkirane, A., Douieb, J., Val, M. Ould Mohamedhen: An approximation theorem in Musielak-Orlicz-Sobolev spaces. Commentat. Math. 51 (2011), 109-120. | DOI | MR | JFM

[3] Benkirane, A., Val, M. Ould Mohamedhen: Some approximation properties in Musielak-Orlicz-Sobolev spaces. Thai J. Math. 10 (2012), 371-381. | MR | JFM

[4] Bennett, C., Sharpley, R.: Interpolation of Operators. Pure and Applied Mathematics 129, Academic Press, Boston (1988). | DOI | MR | JFM

[5] Cruz-Uribe, D., Fiorenza, A.: Approximate identities in variable $L^{p}$ spaces. Math. Nachr. 280 (2007), 256-270. | DOI | MR | JFM

[6] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics 2017, Springer, Berlin (2011). | DOI | MR | JFM

[7] Hudzik, H.: A generalization of Sobolev spaces. II. Funct. Approximatio, Comment. Math. 3 (1976), 77-85. | MR | JFM

[8] Kamińska, A.: On some compactness criterion for Orlicz subspace $E_{\Phi}(\Omega)$. Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 22 (1981), 245-255. | DOI | MR | JFM

[9] Kamińska, A.: Some convexity properties of Musielak-Orlicz spaces of Bochner type. Rend. Circ. Mat. Palermo, II. Ser. Suppl. 10 (1985), 63-73. | MR | JFM

[10] Kamińska, A., Hudzik, H.: Some remarks on convergence in Orlicz space. Commentat. Math. 21 (1980), 81-88. | DOI | MR | JFM

[11] Kamińska, A., Kubiak, D.: The Daugavet property in the Musielak-Orlicz spaces. J. Math. Anal. Appl. 427 (2015), 873-898. | DOI | MR | JFM

[12] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czech. Math. J. 41 (1991), 592-618. | DOI | MR | JFM

[13] Krasnosel'skiĭ, M. A., Rutitskiĭ, J. B.: Convex Functions and Orlicz Spaces. P. Noordhoff, Groningen (1961). | MR | JFM

[14] Kufner, A., John, O., Fučík, S.: Function Spaces. Monographs and Textbooks on Mechanics of Solids and Fluids. Mechanics: Analysis, Noordhoff International Publishing, Leyden; Academia, Prague (1977). | MR | JFM

[15] Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics 1034, Springer, Berlin (1983). | DOI | MR | JFM

[16] Nakano, H.: Modulared Semi-Ordered Linear Spaces. Tokyo Math. Book Series 1, Maruzen, Tokyo (1950). | MR | JFM

[17] Orlicz, W.: Über konjugierte Exponentenfolgen. Studia Math. German 3 (1931), 200-211. | DOI | JFM

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