Regularization of p-Adic Distributions Associated to Functions on p-Adic Fields With Moderate Variation

Abstract

The p-adic distributions attached to ordinary functions defined on p-adic fields with moderate variation are studied. We first give a sufficient growth condition on ordinary functions to construct p-adic distributions. Then a moderate variation condition on functions for regularization of these p-adic distributions is imposed which provides a general method to construct p-adic measures. The p-adic integrals against these measures are also explicitly transformed to integrals against Bernoulli measures. © 2024 Elsevier B.V., All rights reserved.