Our professor the other day wrote the following on the blackboard: "Let $u(x)=(v(x),w(x))$ be such that $u \in H^{2,1}$ where $H^{2,1}=H^2 \oplus H^1$." He then mumbled something about this space which I failed to hear. Due to silly me, getting embarassed to ask questions in front of an audience, I didn't raise my hand. So here I am, asking:
Is this the direct sum of the Hilbert spaces $H^k=W^{k,2}$? What is the respective norm, i.e how do I interpret $\| u\|_{H^{2,1}}$?
Many thanks in advance for any help and merry Christmas!