  In this paper we introduce the concept of Bochner pg-frames for Banach
spaces. We characterize the Bochner pg-frames and specify the optimal bounds of
a Bochner pg- frames. Then we define a Bochner qg-Riesz basis and verify the
relations between Bochner pg-frames and Bochner qg-Riesz bases. Finally, we
discuss the perturbation of Bochner pg-frames.
