| Title:
|
Further remarks on the Nemitskii operator in Hölder spaces (English) |
| Author:
|
Nugari, Rita |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
89-95 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper is concerned with the Nemitskii operator in Hölder spaces. Namely conditions are given to ensure acting, continuity, Lipschitz and differentiability properties. (English) |
| Keyword:
|
Nemitskii operator |
| Keyword:
|
Hölder spaces |
| MSC:
|
46E35 |
| MSC:
|
47H15 |
| MSC:
|
47H30 |
| MSC:
|
47J05 |
| idZBL:
|
Zbl 0806.47061 |
| idMR:
|
MR1240207 |
| . |
| Date available:
|
2009-01-08T18:01:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118559 |
| . |
| Reference:
|
[1] Appell J.: The superposition operator in function spaces - A survey.Expo. Math. 6 (1975), 209-270. MR 0949784 |
| Reference:
|
[2] Appell J., Zabreiko P.: Nonlinear superposition operators.Cambridge Tracts in Mathematics 95, Cambridge University Press, 1990. MR 1066204 |
| Reference:
|
[3] Bondarenko V.A., Zabreiko P.: The superposition operator in Hölder function spaces.Soviet Math. Dokl. 16 (1975), 739-743. |
| Reference:
|
[4] Drábek P.: Continuity of Němickij's operator in Hölder spaces.Comment. Math. Univ. Carolinae 16 (1975), 37-57. MR 0380547 |
| Reference:
|
[5] Goebel M.: On Fréchet differentiability of Nemitskij operators acting in Hölder spaces.Glasgow Math. J. 33 (1991). MR 1089947 |
| Reference:
|
[6] Goebel M.: Continuity and Fréchet differentiability of Nemitskij operators in Hölder spaces.Monatshefte für Mathematik 113 (1992), 107-119. MR 1154474 |
| Reference:
|
[7] Nugari R.: Continuity and differentiability properties of the Nemitskij operator in Hölder spaces.Glasgow Math. J. 30 (1988), 59-65. MR 0925559 |
| Reference:
|
[8] Valent T.: Boundary value problems in finite elasticity.Springer Tracts in Natural Philosophy 31, Springer-Verlag, New York, 1988. MR 0917733 |
| . |
