Boundedness of the discrete square function on nondoubling parabolic manifolds with ends

Abstract

Let M be a nondoubling parabolic manifold with ends. In this study, we will investigate the Lp boundedness of the discrete square function in terms of the Littlewood-Paley decomposition. It should be pointed out that, in our setting, the doubling condition of the underlying space and the regularity estimate of the kernel are missing.