Let
be the -dimensional closed ball of radius
centered at the origin. A function which is defined on
is called an extension to of a function defined on if

(1)

Given 2 Banach spaces of functions defined on
and ,
find the extension operator from one to the other of minimal norm. Mikhlin (1986)
found the best constants such that this condition, corresponding to the Sobolev
integral norm, is satisfied,