Harmonic analysis in the p-adic Lizorkin spaces:: Fractional operators, pseudo-differential equations, p-adic wavelets, Tauberian theorems

In this article the p-adic Lizorkin spaces of test functions and distributions are introduced. Multi-dimensional Vladimirovs and Taibleson's fractional operators, and a class of p-adic pseudo-differential operators are studied on these spaces. Since the p-adic Lizorkin spaces are invariant under these operators, they can ploy a key role in considerations related to fractional operator problems. Solutions of pseudo-differential equations are also constructed. Some problems of spectral analysis of pseudo-differential operators are studied. p-Adic multidimensional Tauberian theorems connected with these pseudo-differential operators for the Lizorkin distributions are proved.