Recent Progress in Hardy Spaces on Manifolds

Abstract

In this paper, we introduce a kind of Hardy spaces HΦ(M) on a connected complete Riemannian manifold M with nonnegative Ricci curvature, set up two characterizations of HΦ(M) for H-increasing function Φ, and, make some brief discussions about Lipschitz spaces Λα(M) (α > 0) and dual of HΦ(M) for Φ(x) = xP (0 < p ≤ 1). At same time, we set up some distribution inequalities about radial maximal function, nontangential maximal function and square function.