# Asymptotic Properties of the p-Adic Fractional Integration Operator

## TL;DR

This paper investigates the long-term behavior of a p-adic fractional integration operator, extending previous work on non-Archimedean pseudo-differential equations to understand its asymptotic properties.

## Contribution

It provides a detailed analysis of the asymptotic properties of the p-adic fractional integration operator, a novel extension of Kochubei's earlier work.

## Key findings

- Characterization of the asymptotic behavior of the operator
- Identification of conditions for specific asymptotic regimes
- Extension of classical fractional integration results to p-adic context

## Abstract

We study asymptotic properties of the p-adic version of a fractional integration operator introduced in the paper by A. N. Kochubei, Radial solutions of non-Archimedean pseudo-differential equations, Pacif. J. Math. 269 (2014), 355-369.