Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm
Hudzik, Henryk ; Landes, Thomas
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 615-621 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this paper we extend the result of [6] on the characteristic of convexity of Orlicz spaces to the more general case of Musielak-Orlicz spaces over a non-atomic measure space. Namely, the characteristic of convexity of these spaces is computed whenever the Musielak-Orlicz functions are strictly convex.

Publié le : 1992-01-01
Classification:  46B20,  46E30 
@article{118532,
     author = {Henryk Hudzik and Thomas Landes},
     title = {Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {615-621},
     zbl = {0779.46029},
     mrnumber = {1240182},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118532}
}

Hudzik, Henryk; Landes, Thomas. Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 615-621. http://gdmltest.u-ga.fr/item/118532/

Chen S.; Hudzik H. On some convexities of Orlicz and Orlicz-Bochner spaces, Comment. Math. Univ. Carolinae 29 (1988), 13-29. (1988) | MR 0937545 | Zbl 0647.46030

Diestel J. Sequences and Series in Banach Spaces, Springer, 1964. | MR 0737004

Hudzik H. On some equivalent conditions in Musielak-Orlicz spaces, Commentationes Math. (Prace Matemat.) 24 (1984), 57-64. (1984) | MR 0759055 | Zbl 0564.46022

Hudzik H. Uniform convexity of Musielak-Orlicz spaces with Luxemburg's norm, Commentationes Math. (Prace Matemat.) 23 (1983), 21-32. (1983) | MR 0709167 | Zbl 0595.46027

Hudzik H.; Kaminska A. Some remarks on convergence in Orlicz spaces, Commentationes Math. (Prace Matemat.) 21 (1979), 81-88. (1979) | MR 0577673

Hudzik H.; Kaminska A.; Musielak J. On the convexity coefficient of Musielak-Orlicz spaces, Math. Zeitschr. 197 (1988), 291-295. (1988) | MR 0923496

Krasnoselskii M.A.; Rutickii Ya.B. Convex Functions and Orlicz Spaces, translation, Groningen, 1961.

Lindenstrauss J.; Tzafriri L. Classical Banach Spaces II - Function Spaces, Springer, 1979. | MR 0540367 | Zbl 0403.46022

Luxemburg W.A.J. Banach function spaces, PhD thesis, Delft, 1955. | MR 0072440 | Zbl 0162.44701

Musielak J. Orlicz Spaces and Modular Spaces, Springer, 1983. | MR 0724434 | Zbl 0557.46020

Musielak J.; Orlicz W. On modular spaces, Stud. Math. 18 (1959), 49-65. (1959) | MR 0101487 | Zbl 0099.09202