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Zeitschrift für Analysis und ihre Anwendungen

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Volume 18, Issue 4, 1999, pp. 839–848
DOI: 10.4171/ZAA/917

Published online: 1999-12-31

On Direct Decomposition of the Space $\mathcal L_p(\Omega)$

Uwe Kähler[1]

(1) Universidade de Aveiro, Portugal

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.

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

Kähler Uwe: On Direct Decomposition of the Space $\mathcal L_p(\Omega)$. Z. Anal. Anwend. 18 (1999), 839-848. doi: 10.4171/ZAA/917