The \(L^r\)-variational integral (Q2120548)

The authors define and investigate the \(L^r\)-variational integral which recovers a function from its \(L^r\)-derivative [\textit{L. Gordon}, Stud. Math. 28, 295--316 (1967; Zbl 0152.24605)]. It is proved that, similarly to the classical case, the \(L^r\)-variational integral is equivalent to the \(HK_r\)-integral introduced in [\textit{P. M. Musial} and \textit{Y. Sagher}, Stud. Math. 160, No. 1, 53--81 (2004; Zbl 1063.26004)].