| Title:
|
Extending $n$ times differentiable functions of several variables (English) |
| Author:
|
Fejzić, Hajrudin |
| Author:
|
Rinne, Dan |
| Author:
|
Weil, Clifford |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
825-830 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that $n$ times Peano differentiable functions defined on a closed subset of $\mathbb{R}^m$ and satisfying a certain condition on that set can be extended to $n$ times Peano differentiable functions defined on $\mathbb{R}^m$ if and only if the $n$th order Peano derivatives are Baire class one functions. (English) |
| MSC:
|
26A21 |
| MSC:
|
26B05 |
| idZBL:
|
Zbl 1005.26007 |
| idMR:
|
MR1746707 |
| . |
| Date available:
|
2009-09-24T10:28:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127531 |
| . |
| Reference:
|
[ALP1985] V. Aversa, M. Laczkovich, D. Preiss: Extension of differentiable functions.Comment. Math. Univ. Carolin. 26 (1985), 597–609. MR 0817830 |
| Reference:
|
[BW1996] Z. Buczolich and C. E. Weil: Extending Peano differentiable functions.Atti Sem. Mat. Fis. Univ. Modena 44 (1996), no. 2, 323–330. MR 1428765 |
| Reference:
|
[FMW1994] H. Fejzić, J. Mařík and C. E. Weil: Extending Peano derivatives.Math. Bohemica 119 (1994), 387–406. MR 1316592 |
| Reference:
|
[FR1996] H. Fejzić and D. Rinne: Continuity properties of Peano derivatives in several variables.Real Analysis Exch. 21 (1995–96), 292–298. MR 1377538 |
| Reference:
|
[H1962] F. Hausdorff: Set Theory.Chelsea, 1962. MR 0141601 |
| Reference:
|
[J1923] V. Jarník: Sur l’extension du domaine de definition des fonctions d’une variable, qui laisse intacte la derivabitité de la fonction.Bull international de l’Acad Sci de Boheme (1923). |
| Reference:
|
[M1984] J. Mařík: Derivatives and closed sets.Acta Math. Hungar. 43 (1984), 25–29. MR 0731958, 10.1007/BF01951320 |
| Reference:
|
[PL1974] G. Petruska and M. Lackovich: Baire 1 functions, approximately continuous functions and derivatives.Acta Math. Acad Sci. Hungar. 25 (1974), 189–212. MR 0379766, 10.1007/BF01901760 |
| Reference:
|
[S1970] E. M. Stein: Singular integrals and differentiability properties of functions.Princeton University Press, Princeton, NJ, USA, 1970. Zbl 0207.13501, MR 0290095 |
| . |
