The three-line theorem on the octonions is obtained, which generalizes the result of J.Peetre and P. Sjoelin from the associative Clifford algebra to non-associative octonion algebra.
Let D be the unit disk in the complex plane with the weighted measure dμβ(z) = (β+1)--π(1-|z|2)βdm(z)(β＞-1). Then L2(D,dμβ(z)) = ∞k=0(Aβk Aβk) is the orthogonal direct sum decomposition.In this paper, we define the Hankel and Toeplitz type operators, and study the boundedness, compactness and Sp-criteria for them.
