p-Adic analysis in the Lizorkin type spaces: fractional operators, pseudo-differential equations and Tauberian theorems

Albeverio, S.; Khrennikov, A. Yu.; Shelkovich, V. M.

p-Adic analysis in the Lizorkin type spaces: fractional operators, pseudo-differential equations and Tauberian theorems

Authors

Albeverio, S.

Khrennikov, A. Yu.

Shelkovich, V. M.

Description

In this paper the p -adic Lizorkin spaces of test functions and distributions are introduced, and multidimensional Vladimirov's and Taibleson's fractional operators are studied on these spaces. Since the p -adic Lizorkin spaces are invariant under the Vladimirov and Taibleson operators, they can play a key role in considerations related to fractional operator problems. A class of p -adic pseudo-differential operators in the Lizorkin spaces is also introduced and solutions of pseudo-differential equations are constructed. p -Adic multidimensional Tauberian theorems connected with fractional operators and pseudo-differential operators for the Lizorkin distributions are also proved.
32 pages