The Helmholtz decomposition of a space of vector fields with bounded mean oscillation in a bounded domain
Yoshikazu Giga, Zhongyang Gu · Mathematische Annalen · 2022
Abstract We introduce a space of vector fields with bounded mean oscillation whose “tangential” and “normal” components to the boundary behave differently. We establish its Helmholtz decomposition when the domain is bounded. This substantially extends the authors’ earlier result for a half space.