Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm
Henryk Hudzik; L. Wang; Ting Fu Wang
Commentationes Mathematicae Universitatis Carolinae (2001)
- Volume: 42, Issue: 3, page 487-497
- ISSN: 0010-2628
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topHudzik, Henryk, Wang, L., and Wang, Ting Fu. "Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 487-497. <http://eudml.org/doc/248772>.
@article{Hudzik2001,
abstract = {First, we extend the criteria for smooth points of $S(L_\{M\})$ from [22] to the whole class of Musielak-Orlicz spaces. Next, we present criteria for very smooth and strongly smooth points of $S(L_\{M\})$.},
author = {Hudzik, Henryk, Wang, L., Wang, Ting Fu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {smooth points; very smooth points; strongly smooth points; Musielak-Orlicz function spaces; Luxemburg norm; smooth points; very smooth points; strongly smooth points; Luxemburg norm},
language = {eng},
number = {3},
pages = {487-497},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm},
url = {http://eudml.org/doc/248772},
volume = {42},
year = {2001},
}
TY - JOUR
AU - Hudzik, Henryk
AU - Wang, L.
AU - Wang, Ting Fu
TI - Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 487
EP - 497
AB - First, we extend the criteria for smooth points of $S(L_{M})$ from [22] to the whole class of Musielak-Orlicz spaces. Next, we present criteria for very smooth and strongly smooth points of $S(L_{M})$.
LA - eng
KW - smooth points; very smooth points; strongly smooth points; Musielak-Orlicz function spaces; Luxemburg norm; smooth points; very smooth points; strongly smooth points; Luxemburg norm
UR - http://eudml.org/doc/248772
ER -
References
top- Bian S., H. Hudzik., Wang T., Smooth, very smooth and strongly smooth points in Musielak-Orlicz sequence spaces, Bull. Austral. Math. Soc. 63 (2001), 441-457. (2001) Zbl0987.46004MR1834945
- Chen S., Geometry of Orlicz spaces, Dissertationes Math. 356 (1996), 1-204. (1996) Zbl1089.46500MR1410390
- Chen S., Smoothness of Orlicz spaces, Comment. Math. 27 (1987), 49-58. (1987) Zbl0641.46010MR0910960
- Chen S., Hudzik H., Kamińska A., Support functionals and smooth points in Orlicz function spaces equipped with the Orlicz norm, Math. Japonica 39.2 (1992), 271-279. (1992) MR1270637
- Chen S., Hudzik H., Wisła M., Smooth points in Orlicz sequence spaces and geometry of the dual and the bidual of Orlicz spaces, Math. Japonica 44.2 (1996), 367-375. (1996) MR1416279
- Diestel J., Geometry in Banach spaces - selected topics, Lecture Notes in Math. 485, Springer Verlag, 1975. MR0461094
- Grząślewicz R., Hudzik H., Smooth points of Orlicz spaces equipped with Luxemburg norm, Math. Nachr. 155 (1992), 31-45. (1992) MR1231254
- Hudzik H., Liu L., Wang T., Uniformly Gateaux differentiability of Musielak-Orlicz spaces, to appear.
- Hudzik H., Ye Y., Support functionals and smoothness in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, Comment. Math. Univ. Carolinae 31.4 (1990), 661-684. (1990) MR1091364
- Hudzik H., Zbąszyniak Z., Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, Colloquium Math. 65.2 (1993), 157-164. (1993) MR1240162
- Hudzik H., Zbąszyniak Z., Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm, Collectanea Math. 48 (4-6) (1998), 543-567. (1998) MR1602592
- Krasnoselskiĭ M.A., Rutickiĭ Ya.B., Convex Functions and Orlicz Spaces, Groningen, 1961 (translation).
- Luxemburg W.A.J., Banach function spaces, Thesis, Delft 1955. Zbl0162.44701MR0072440
- Maligranda L., Orlicz spaces and interpolation, Seminars in Mathematics, Campinas SP (Brasil), 1989. Zbl0874.46022MR2264389
- Musielak J., Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, 1983. Zbl0557.46020MR0724434
- Płuciennik R., Ye Y., Differentiability of Musielak-Orlicz sequence spaces, Comment. Math. Univ. Carolinae 30.4 (1989), 699-711. (1989) MR1045898
- Rao M.M., Ren Z.D., Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. Zbl0724.46032MR1113700
- Wang T., Bian S., Smooth and strong (very) smooth points in Musielak-Orlicz function spaces equipped with the Orlicz norm, Chi. Acta Appl. Funct. Anal. 1 (1) (1999), 61-68. (1999) MR1739240
- Wang T., Hao C., Liu L., Smooth and strong (very) smooth points in Musielak-Orlicz sequence spaces equipped with the Orlicz norm, Math. Adv., to appear.
- Wang T., Shi Z., On the locally uniformly weak star rotundity of Orlicz spaces, Revista Math. Complutense 7 (1994), 79-98. (1994) Zbl0804.46038MR1277331
- Wu C., Sun S., Norm calculation and complex convexity of the Musielak-Orlicz sequence space, Chinese Ann. Math. 12A (1991), suppl., 98-102. (1991) MR1118272
- Zbąszyniak Z., Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm, Comment. Math. Univ. Carolinae 35.1 (1994), 95-102. (1994) MR1292586
- Zbąszyniak Z., Smoothness of Musielak-Orlicz sequence spaces equipped with the Orlicz norm, Proc. Intern. Conf. ``Function Spaces V'', Poznań, August 28 - September 1, 1998, Marcel Dekker, to appear. MR1772151
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