\(L^ p\)-analysis on homogeneous manifolds of reductive type and representation theory (Q1364462)

\(L^p\)-analysis on homogeneous manifolds of reductive type and representation theory are discussed. The main results are: Let \(G\) be a real reductive linear Lie group, \(K\) a maximal compact subgroup of \(G\), and \(\theta\) the corresponding Cartan involution, \(H\) a closed \(\theta\)-stable subgroup of \(G\) with finitely many connected components. There are four sections in this paper: (1) Invariant measures on homogeneous manifolds of reductive type. (2) Irreducible representations in \(L^p(G/H)\). (3) Holomorphic discrete series representations. (4) Some valuable examples are given.