## Asymptotic properties of the $$p$$-adic fractional integration operator.(English)Zbl 1389.11140

A. N. Kochubei [Pac. J. Math. 269, No. 2, 355–369 (2014; Zbl 1396.35070)] introduced a right inverse $$I^\alpha$$ of Vladimirov’s fractional differentiation operator $$D^\alpha$$ ($$\alpha >0$$) acting on complex-valued functions on the field of $$p$$-adic numbers. $$I^\alpha$$ can be seen as a $$p$$-adic counterpart of the Riemann-Liouville fractional integral of real analysis. In this paper, the authors study asymptotic properties of $$I^\alpha f$$, given the asymptotics of a function $$f$$. See S. G. Samko et al. [Fractional integrals and derivatives: theory and applications. New York, NY: Gordon and Breach. xxxvi, 976 p. (1993; Zbl 0818.26003)] for results of this kind for the Riemann-Liouville integration operator.

### MSC:

 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 26A33 Fractional derivatives and integrals

### Citations:

Zbl 0818.26003; Zbl 1396.35070
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