  We develop an analysis of wavelets and pseudodifferential operators on
multidimensional ultrametric spaces which are defined as products of locally
compact ultrametric spaces. We introduce bases of wavelets, spaces of
generalized functions and Lizorkin generalized functions on multidimensional
ultrametric spaces.
  We also consider some family of pseudodifferential operators on
multidimensional ultrametric spaces. The notions of Cauchy problem for
ultrametric pseudodifferential equations and of ultrametric characteristics are
introduced. A theorem about existence and uniqueness of the solution for the
Cauchy problem (the analogue of the Kovalevskaya theorem) is proven.
