Hardy Inequality On H-type Group, The Pohozaev Identity And A Unique Extension,

This paper is devoted to the study of some properties on groups of Heisenberg type.Chapter One gives several Hardy inequalities on groups of Heisenberg type. The best constant in Hardy inequality for the sub-Laplacian is determined.In Chapter Two, some integral identities on groups of Heisenberg type are established. A nonexistence result for posotive solutions of semilinear sub-Laplace equations on groups of Heisenberg type is obtained.In Chapter Three, a Carleman estimation for the sub-Laplacian on groups of Heisenberg type is found and a unique continuation theorem is proved.