Norms and derivatives (Q1308831)

The paper is a continuation of \textit{J. Mařík} and \textit{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.