Mařík, Jan Norms and derivatives. (English) Zbl 0787.26009 Real Anal. Exch. 18(1992/93), No. 2, 343-351 (1993). The paper is a continuation of J. Mařík and C. E. Weil [Proc. Am. Math. Soc. 112, No. 3, 807-817 (1991; Zbl 0746.26002)]. The aim is to study conditions under which the square root of the sum of squares of two derivatives is still a derivative. The conditions are formulated in terms of multiplicative families for bounded approximately continuous functions and stated in Theorem 6.2 (even in greater generality for \(p>0\)). The paper includes also some negative results and generalizations for \(n\)-tuples of derivatives. Reviewer: J.Niewiarowski (Łódź) MSC: 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable Keywords:sums of powers of derivatives; square root; sum of squares of two derivatives; multiplicative families; bounded approximately continuous functions Citations:Zbl 0746.26002 × Cite Format Result Cite Review PDF