摘要：

Spectral Turan problems for graphs have been studied extensively and analogues of Turan problems for hypergraphs have appeared in the literature. In this talk, We continue to consider hypergraph spectral Turan problem. We shall show that among all K_l^(k)-free k-graphs on n vertices, the r-partie k-uniform Turan hypergraph (balanced complete r-partite k-uniform) attains the maximal p-spectral radius. This is a p-spectral analogues of the hypergraph Turan problem by Mubayi and Pikhurko [JCTB, 97 (2007) 669-678]. In addition we also provide a generalizations of the hypergraph spectral Turan problem on vector spaces over finite field.