  A new Hardy space Hardy space approach of Dirichlet type problem based on
Tikhonov regularization and Reproducing Hilbert kernel space is discussed in
this paper, which turns out to be a typical extremal problem located on the
upper upper-high complex plane. If considering this in the Hardy space, the
optimization operator of this problem will be highly simplified and an
efficient algorithm is possible. This is mainly realized by the help of
reproducing properties of the functions in the Hardy space of upper-high
complex plane, and the detail algorithm is proposed. Moreover, harmonic
mappings, which is a significant geometric transformation, are commonly used in
many applications such as image processing, since it describes the energy
minimization mappings between individual manifolds. Particularly, when we focus
on the planer mappings between two Euclid planer regions, the harmonic mappings
are exist and unique, which is guaranteed solidly by the existence of harmonic
function. This property is attractive and simulation results are shown in this
paper to ensure the capability of applications such as planer shape distortion
and surface registration.
