Geodesic
On extensions of inequalities of Kolmogoroff and others and some applications to almost periodic functions
Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 1-16

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Let f(x) be a complex function of a real variable, defined over the whole real line, which possesses n derivatives (the nth at least almost everywhere) and is such that . Then, if k is any integer for which 0< k < n, Kolmogoroff's inequality may be written as,or, by putting ,The constant K=K (k, n) known explicitly and is the best possible, i.e., there is a (real) function for which equality holds (see Bang [1]). 
Upton, C. J. F. On extensions of inequalities of Kolmogoroff and others and some applications to almost periodic functions. Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 1-16. doi: 10.1017/S0017089500001300
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