Pseudodifferential <Emphasis Type="Italic">p</Emphasis>-adic vector fields and pseudodifferentiation of a composite <Emphasis Type="Italic">p</Emphasis>-adic function

We discuss transformation of p-adic pseudodifferential operators (in the one-dimensional and multidimensional cases) with respect to p-adic maps which correspond to automorphisms of the tree of balls in the corresponding p-adic spaces. In the dimension one we find a rule of transformation for pseudodifferential operators. In particular we find the formula of pseudodifferentiation of a composite function with respect to the Vladimirov p-adic fractional operator. We describe the frame of wavelets for the group of parabolic automorphisms of the tree T (O _p ) of balls in O _p . In many dimensions we introduce the group of mod p-affine transformations, the family of pseudodifferential operators corresponding to pseudodifferentiation along vector fields on the tree T (O _p ) and obtain a rule of transformation of the introduced pseudodifferential operators with respect to mod p-affine transformations.