In the paper Differentiability of a function and of its compositions with functions of one variable, Jan Boman proves the following theorem:
Let be a function from to , and assume that the composed function belongs to for every . Then .
The theorem is quoted with a proof in The convenient setting of global analysis by Kriegl and Michor (theorem 3.4).
Jan Boman, Differentiability of a function and of its compositions with functions of one variable, Math. Scand. 20 1967 249–268, MR237728 pdf
Andreas Kriegl, Peter W. Michor, The convenient setting of global analysis, Math. Surveys and Monographs 53, Amer. Math. Soc. 1997. x+618 pp. ISBN: 0-8218-0780-3 html MR1471480
Revised on November 10, 2012 02:06:15
by Zoran Škoda