On Direct Decomposition of the Space ${\mathcal{L}}_p(\Omega )$

Abstract

A direct decomposition of the space ${\mathcal{L}}_p(\Omega )$ is obtained as a generalization of the orthogonal decomposition of the space ${\mathcal{L}}_2(\Omega )$, where one of the subspaces is the space of all monogenic ${\mathcal{L}}_p$-functions. Basic results about the orthogonal decomposition are carried over to this more general context. In the end a boundary value problem of the Stokes equations will be studied by a method based on this direct decomposition.