A vanishing theorem and
periodicity theorem for the classical mod2 Adams spectral sequence were originally
proved by Adams [1]. The results were extended to the unstable range by Bousfield
[2]. The purpose of this paper is to show the analogue of Bousfield’s work for the
modp unstable Adams spectral sequence of Massey-Peterson type (called
the modp Massey-Peterson spectral sequence), where p is an odd prime.
The results generalized those obtained by Liulevicius [5], [6] to the unstable
range. As an immediate topological application we have the estimation of the
upper bounds of the orders of elements in the p-primary component of the
homotopy groups of, for example, an odd dimensional sphere, Stiefel manifold, or
H-space.
