Boundedness of some singular integrals on nondoubling parabolic manifolds with ends

In this thesis, we aim to study the boundedness of some singular integrals with nonsmooth kernels on nondoubling spaces. More specifically, we study the boundedness of the maximal functions associated with the heat semi-group, the holomorphic functional calculus of Laplace transform type and the square function in terms of the Littlewood-Paley decomposition on nondoubling parabolic manifolds with ends. It should be pointed out that, in our setting, the doubling condition of the underlying spaces as well as the regularity estimates of the kernels are missing.