Besov spaces and Bessel potential spaces on certain groups (Q1178759)

Let \(G\) denote a non-compact Vilenkin group, that is, \(G\) is a locally compact, non-compact, Abelian topological group containing a strictly decreasing sequence of compact open subgroups \((G_ n)^ \infty_{- \infty}\) such that \(\cup_{-\infty}^ \infty G_ n = G\), \(\cap^ \infty_{-\infty} G_ n = \{0\}\) and \(\sup_ n[G_ n : G_{n=1}] < \infty\). The author defines (inhomogeneous) Besov spaces \(B(\alpha, p, s;G)\), \(\alpha\varepsilon\mathbb{R}\), \(0 < p,s \leq \infty\), and Bessel potential spaces \(h^ p_ \alpha(G)\), \(\alpha\in\mathbb{R}\), \(0 < p < \infty\), on these groups and announces a number of results for these spaces. The results range from interpolation theorems for both the real and complex interpolation method, to embedding theorems for various Bessel potential or Besov spaces and to results for convoluteurs between some of these spaces. The paper does not contain proofs of the theorems; these will appear elsewhere.