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.
Table of Contents1. Introduction -- 2. Calderón-Zygmund operators on spaces of homogenous type -- 3. Singular integrals beyond Calderón-Zygmund theory -- 4. Maximal functions on nondoubling parabolic manifolds with ends -- 5. Functional calculus of Laplace transform type on nondoubling parabolic manifolds with ends -- 6. The Littlewood-Paley inequalities on nondoubling parabolic manifolds with ends -- Bibliography
NotesA thesis submitted to Macquarie University for the degree of Doctor of Philosophy
Includes bibliographical references (pages 127-131)
Awarding InstitutionMacquarie University
Degree TypeThesis PhD
DegreeThesis (PhD), Macquarie University, Department of Mathematics and Statistics, 2020
Department, Centre or SchoolDepartment of Mathematics and Statistics
Year of Award2020
Principal SupervisorXuan Thinh Duong
Additional Supervisor 1Ji Li
RightsCopyright disclaimer: https://www.mq.edu.au/copyright-disclaimer
Copyright Hong Chuong Doan 2020.
Extentx, 131 pages