On a Direct Decomposition of the Space ${\cal L}_p(\Omega$

U. Kähler

Abstract: A direct decomposition of the space ${\cal L}_p(\Omega)$ is obtained as a generalization of the orthogonal decomposition of the space ${\cal L}_2 (\Omega)$, where one of the subspaces is the space of all monogenic ${\cal L} _p$-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.

Keywords: clifford analysis, $L_p$-decomposition, Stokes equations

Classification (MSC2000): 30G35, 31B10, 30Q30, 46B25

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