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.