On traces of general decomposition spaces (Q368522)

Let \(a=(a_1,\ldots,a_d)\), \(a_k >0\), \(\sum^d_{j=1} a_j =1\), be an anisotropy in \(\mathbb R^d\). Let \(|\xi|_a = \sum^d_{j=1} |\xi_j|^{1/a_j}\) be the related anisotropic distance in \(\mathbb R^d\). The author introduces for a fixed \(a\) anisotropic spaces \(F^s_{p,q} (\mathbb R^d)\) and \(B^s_{p,q}({\mathbb R^d}) =M^s_{p,q} (\mathbb R^d)\) using dyadic resolutions of unity based on related dyadic anisotropic annuli. Here, \(s\in \mathbb R\), \(0<p \leq \infty\) (\(p<\infty\) for \(F\)-spaces), \(0<q\leq \infty\). The paper deals with traces of these spaces on the hyperplane \(\mathbb R^{d-1}\).