| Title:
|
Characterization of globally Lipschitzian composition operators in the Banach space ${\rm BV}\sb p\sp 2[a,b]$ (English) |
| Author:
|
Matkowski, Janusz |
| Author:
|
Merentes, Nelson |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
181-186 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a characterization of the globally Lipschitzian composition operators acting in the space $BV_p^2[a,b]$ (English) |
| Keyword:
|
Riesz space |
| Keyword:
|
bounded p-variation |
| Keyword:
|
globally Lipschitzian composition operator |
| MSC:
|
26A16 |
| MSC:
|
39B22 |
| MSC:
|
46E15 |
| MSC:
|
47H09 |
| MSC:
|
47H30 |
| idZBL:
|
Zbl 0785.47033 |
| idMR:
|
MR1222285 |
| . |
| Date available:
|
2008-06-06T21:22:44Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107449 |
| . |
| Reference:
|
[1] Knop, J.: On globally Lipschitzian operator in the space $\text{Lip} C^r[a,b]$.Fasculi Math. 21 (1990), 79-85. MR 1115522 |
| Reference:
|
[2] Matkowska, A.: On characterization of Lipschitzian operators of substitution in the class of Hölder’s function.Zeszyty Naukowe Politechniki Lodzkiej, Matematyka. Z. 17 (1984), 81-85. MR 0790842 |
| Reference:
|
[3] Matkowski, J.: Functional Equations and Nemyskij operators.Funkcialaj Ekvacioj 25 (1982), 127-132. MR 0694906 |
| Reference:
|
[4] Matkowski, J.: Form of Lipschitzian operator of substitution in Banach space of differentiable functios.Zeszyty Naukowe Politechniki-Lódzkiej, Matematyka. Z. 17 (1984), 5-10. MR 0790835 |
| Reference:
|
[5] Matkowski, J., Miś, J.: On a characterization of Lipschitzian operators of substitution in the space $BV[a,b]$.Math. Nach. 117 (1984), 155-159. MR 0755299 |
| Reference:
|
[6] Merentes, N.: On a characterization of Lipschitzian operators of substitution in the space of bounded Riesz $\varphi $-variation.Ann. Univ. Sci. Budapest. Sect. Math. (to appear). Zbl 0808.47050, MR 1161510 |
| Reference:
|
[7] Merentes, N.: On the concept of bounded $(p,2)$-variation of a function.Rend. Sem. Mat. Univ. Padova (submitted). |
| Reference:
|
[8] Riesz, F.: Untersuchungen über systeme intergrierbarer functionen.Mathematische Annalen 69 (1910), 1449-1497. |
| Reference:
|
[9] Roberts, A.W., Varberg, D.E.: Convex functions.Academic Press, New York and London, 1973. MR 0442824 |
| Reference:
|
[10] Vallé Poussin, Ch.J. de.: Sur la convergence des formules d’interpolation entre ordinées equidistances.Bull. Acad. Sci. Belg. (1908), 319-410. |
| . |
