  In [Hut16], Hutchings uses embedded contact homology to show the following
for area-preserving disc diffeomorphisms that are a rotation near the boundary
of the disc: If the asymptotic mean action on the boundary is bigger than the
Calabi invariant, then the infimum of the mean action of the periodic points is
less than or equal to the Calabi invariant. In this note, we extend this to
area-preserving disc diffeomorphisms, which are only a rotation on the boundary
of the disc. Our strategy is to extend the diffeomorphism to a larger disc with
nice properties and apply Hutchings' theorem. As a corollary, we observe that
Hutchings' inequality holds for disc diffeomorphisms with a Diophantine
rotation number on the boundary. Finally, as an application we show that in
almost all cases the Calabi invariant of a smooth pseudo-rotation is equal to
its rotation number.
