  We improve the integrability of the state space of the $\Phi ^4_3$-process
and the support of the $\Phi ^4_3$-measure on the torus obtained in [Albeverio,
Kusuoka, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2020]. For the improvement,
we improve the estimates of the H\"older continuity in time of the solutions to
approximation equations. In the present paper, we only discuss the estimates
different from those in [Albeverio, Kusuoka, Ann. Sc. Norm. Super. Pisa Cl.
Sci. (5), 2020].
