Complete function systems and decomposition results arising in Clifford analysis (Q1409785)

The authors construct a Clifford analytic complete system of functions in the generalized Bergman \(p\)-space \(B_{{\mathcal{C}\ell}_{ 0, n}}^{p,\ell} (\Omega)\) where \(\Omega\) is a sufficiently smooth unbounded domain in \(\mathbb{R}^n\). The decomposition \(W_{{\mathcal{C}\ell}_{ 0, n}}^{p,\ell-1}(\Omega) = B_{{\mathcal{C}\ell}_{ 0, n}}^{p,\ell}(\Omega)\oplus D^\ell (W_{{\mathcal{C}\ell}_{ 0, n}}^{0, p, 2\ell-1}(\Omega)), \ell<n, \frac{n}{n-\ell+1}<p<\infty\) for the Sobolew space \(W_{{\mathcal{C}\ell}_{ 0, n}}^{p,\ell-1}\) is considered. Here \(D^\ell\) is the \(\ell\)-th iterate of the Dirac operator.