A modified \(P\)-adic integral and a modified \(P\)-adic derivative for functions defined on a half-axis
The author introduces a generalized Fourier-Walsh transform replacing dyadic decomposition by \(P\)-adic decomposition, where \(P\) is a fixed symmetric subset of \(\mathbb{Z}\). Generalizing the known results for Fourier-Walsh transform he proves several theorems on properties of \(P\)-adic integrals and derivatives and establishes a Hardy type inequality for \(P\)-adic Fourier-Walsh transform.
scientific article; zbMATH DE number 5155798