1. On associated spaces in Clifford analysis
Judith Vanegas
Universidad Sim´on Bol´ıvar
Tallahassee, December 2014
2. Introduction
We say that a function space X is called an associated space to a
given differential operator F if F transforms X into itself.
A simple example: The space of holomorphic functions is
associated to the complex differentiation
d
dz
because the complex
derivative of a holomorphic function is again holomorphic.
3. Associated spaces are used to solve initial value problems of the
type
∂tu = F(t, x, u, ∂j u), j = 0, . . . , n, (1)
u(0, x) = ϕ(x), (2)
where ϕ(x) satisfies the partial differential equation G(u) = 0,
provided that the associated space X of F contains all the
solutions for G(u) = 0, and that the elements of X satisfy an
interior estimate, i.e., an estimate for the derivatives of the
solutions near the boundary of a certain bounded domain.
