## Abstract Let __I__, __J__ ⊂ ℝ be intervals. The main result says that if a superposition operator __H__ generated by a function of two variables __h__: __I__ × __J__ → ℝ, __H__ (__φ__)(__x__) ≔ __h__ (__x__, __φ__ (__x__)), maps the set __BV__ (__I__, __J__) of all bounded variation functions,
✦ LIBER ✦
Superposition operators and functions of bounded p-variation II
✍ Scribed by Gérard Bourdaud; Massimo Lanza de Cristoforis; Winfried Sickel
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 374 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0362-546X
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## Abstract It is known that, if __u__ is a real valued function on ℝ^__N__^ of bounded variation, then its total variation decreases under polarization. In this paper we identify the difference between the total variation of __u__ and that one of its polar __u__~Π~ (© 2009 WILEY‐VCH Verlag GmbH &