| Title:
|
Characteristic of convexity of Musielak-Orlicz function spaces equipped with the Luxemburg norm (English) |
| Author:
|
Hudzik, Henryk |
| Author:
|
Landes, Thomas |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
615-621 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Musielak-Orlicz space |
| Keyword:
|
modulus of convexity |
| Keyword:
|
characteristic of convexity |
| Keyword:
|
the $\Delta _2$-condition |
| MSC:
|
46B20 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 0779.46029 |
| idMR:
|
MR1240182 |
| . |
| Date available:
|
2009-01-08T17:58:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118532 |
| . |
| Reference:
|
[1] Chen S., Hudzik H.: On some convexities of Orlicz and Orlicz-Bochner spaces.Comment. Math. Univ. Carolinae 29 (1988), 13-29. Zbl 0647.46030, MR 0937545 |
| Reference:
|
[2] Diestel J.: Sequences and Series in Banach Spaces.Springer, 1964. MR 0737004 |
| Reference:
|
[3] Hudzik H.: On some equivalent conditions in Musielak-Orlicz spaces.Commentationes Math. (Prace Matemat.) 24 (1984), 57-64. Zbl 0564.46022, MR 0759055 |
| Reference:
|
[4] Hudzik H.: Uniform convexity of Musielak-Orlicz spaces with Luxemburg's norm.Commentationes Math. (Prace Matemat.) 23 (1983), 21-32. Zbl 0595.46027, MR 0709167 |
| Reference:
|
[5] Hudzik H., Kaminska A.: Some remarks on convergence in Orlicz spaces.Commentationes Math. (Prace Matemat.) 21 (1979), 81-88. MR 0577673 |
| Reference:
|
[6] Hudzik H., Kaminska A., Musielak J.: On the convexity coefficient of Musielak-Orlicz spaces.Math. Zeitschr. 197 (1988), 291-295. MR 0923496 |
| Reference:
|
[7] Krasnoselskii M.A., Rutickii Ya.B.: Convex Functions and Orlicz Spaces.translation, Groningen, 1961. |
| Reference:
|
[8] Lindenstrauss J., Tzafriri L.: Classical Banach Spaces II - Function Spaces.Springer, 1979. Zbl 0403.46022, MR 0540367 |
| Reference:
|
[9] Luxemburg W.A.J.: Banach function spaces.PhD thesis, Delft, 1955. Zbl 0162.44701, MR 0072440 |
| Reference:
|
[10] Musielak J.: Orlicz Spaces and Modular Spaces.Springer, 1983. Zbl 0557.46020, MR 0724434 |
| Reference:
|
[11] Musielak J., Orlicz W.: On modular spaces.Stud. Math. 18 (1959), 49-65. Zbl 0099.09202, MR 0101487 |
| . |
