I had just gone to a lecture, and we learned the definition of the Sobolev spaces $W^{k,p}(\Omega)$. We just called this Sobolev space, but my office-mate informed me that most people just call it the Sobolev space $W^{k,p}(\Omega)$, but the exponent $k$ is called the regularity exponent, and $p$ is called the integrability exponent.
We then defined $H^k(\Omega)$ to be $W^{k,2}(\Omega)$ and we remarked that this is a Hilbert space. I was curious if there is a special name for this space like perhaps the "Hilbert-Sobolev space" or something like that, or would I just call it the Sobolev space $H^k(\Omega)$? I couldn't find anything after a quick search, so I thought I would ask here.
