Absolutely continuous functions of several variables and diffeomorphisms

• Autorzy: Stanislav Hencl , Jan Malý
• Języki publikacji: EN

Abstrakty

EN

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.

Słowa kluczowe

EN

absolute continuity in several variables; change of variables; 26B30

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 4
• Strony: 690-705

Daty

wydano

2003-12-01

online

2003-12-01

Twórcy

autor

Stanislav Hencl

• Charles University

autor

Jan Malý

• Charles University

Bibliografia

• [1] M. Csörnyei: “Absolutely continuous functions of Rado, Reichelderfer and Malý”, J. Math. Anal. Appl., Vol. 252, (2000), pp. 147–166. http://dx.doi.org/10.1006/jmaa.2000.6962
• [2] S. Hencl: “On the notions of absolute continuity for functions of several variables”, Fund. Math., Vol. 173, (2002), pp. 175–189. http://dx.doi.org/10.4064/fm173-2-5
• [3] S. Hencl: “Absolutely continuous functions of several variables and quasiconformal mappings”, preprint MATH-KMA-2002/89, Charles University, Prague.
• [4] J. Malý: “Absolutely continuous function of several variables”, J. Math. Anal. Appl., Vol. 231, (1999), pp. 492–508. http://dx.doi.org/10.1006/jmaa.1998.6246

Identyfikatory

DOI

10.2478/BF02475188