On the ultimate Peano derivative (Q5906882)

A real function \(f\) has an \(n\)th generalized Peano derivative at a point \(x\) if there exists a non-negative integer \(k\) such that the \(k\)th primitive of \(f\) has a \((k+n)\)th Peano derivative at \(x\). This notion agrees on compact intervals with absolute Peano derivative introduced by \textit{M. Laczkovich} [in Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 21, 83-97 (1978; Zbl 0425.26005)]. The authors prove that every \(n\)th ultimate Peano derivative [see \textit{C.-M. Lee}, Contemp. Math. 42, 97-103 (1985; Zbl 0575.26004)] is an \(n\)th generalized Peano derivative. This answers the question of C.-M. Lee from the paper mentioned above. The proof of this fact is based on the Tauberian Theorem for Laplace integrals.