A. Gonz\'alez-Enr\'{i}quez and John Vano
An estimate of smoothing and composition with applications to 
conjugation problems
(493K, pdf)

ABSTRACT.  An estimation of the 
difference between smoothing a composition of two 
functions and composing their smoothings is given. 
The smoothing operator considered here is 
defined by the convolution operator 
with a holomorphic kernel. 
It is also shown, by means of an example, 
how apply the estimate given here to obtain 
finite differentiable versions of theorems on 
conjugation of maps in non-perturbative settings.