Inequalities of Littlewood-Paley type for \(n\)-harmonic functions on the polydisk (Q1889630)

A well known result of Littlewood and Paley is the equivalence of the \(L^{p}\) norm of a function~\(f\), holomorphic on the unit disk, and the norm of its \(g\)-function \(g(f)\). The author extends this result to the case where \(f\) is an \(n\)-harmonic function in the polydisk in \(\mathbb{C}^{n}\) and where fractional derivatives are used to define the \(g\)-function.