Abstract
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 nth order Peano derivatives are Baire class one functions.
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References
V. Aversa, M. Laczkovich, D. Preiss: Extension of differentiable functions. Comment. Math. Univ. Carolin. 26 (1985), 597–609.
Z. Buczolich and C. E. Weil: Extending Peano differentiable functions. Atti Sem. Mat. Fis. Univ. Modena 44 (1996), no. 2, 323–330.
H. Fejzić, J. Mařík and C. E. Weil: Extending Peano derivatives. Math. Bohemica 119 (1994), 387–406.
H. Fejzić and D. Rinne: Continuity properties of Peano derivatives in several variables. Real Analysis Exch. 21 (1995–96), 292–298.
F. Hausdorff: Set Theory. Chelsea, 1962.
V. Jarník: Sur 1'extension du domaine de definition des fonctions d'une variable, qui laisse intacte la derivabitité de la fonction. Bull international de 1'Acad Sci de Boheme (1923).
J. Mařík: Derivatives and closed sets. Acta Math. Hungar. 43 (1984), 25–29.
G. Petruska and M. Lackovich: Baire 1 functions, approximately continuous functions and derivatives. Acta Math. Acad Sci. Hungar. 25 (1974), 189–212.
E. M. Stein: Singular integrals and differentiability properties of functions. Princeton University Press, Princeton, NJ, USA, 1970.
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Fejzić, H., Rinne, D. & Weil, C. Extending n times differentiable functions of several variables. Czechoslovak Mathematical Journal 49, 825–830 (1999). https://doi.org/10.1023/A:1022409302825
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DOI: https://doi.org/10.1023/A:1022409302825