In this paper (www.ncbi.nlm.nih.gov/pubmed/18683237) the Sobolev Norm is defined as follows $$ ||f||_l = ||(1 - c \Delta)^{l/2}f||_{L2} $$ $f$ is a function, $\Delta$ is the 2D Laplace and $l$, $c$ are factors.
I can't see how the formal definition of the Sobolev norm (http://mathworld.wolfram.com/SobolevSpace.html) corresponds to the quoted norm... Can anyone help?
It is a special norm that generalizes the characterization of the $H^1$-norm by Fourier transform, this allows you to define the Hilbert-Sobolev spaces $H^s$ with $s \in \mathbb{R}$. That form is a consequence of this fact:
Construction of Sobolev space
The constant $c$ depends on how you define the Fourier transform, in my case $c=1/4\pi$.