H~p Spaces On Tubes

There are four chapters in the dissertation which are consisted of three contents, which are mainly based on Hp theory of complex analysis.which provide the following results:An application of generalized Carleman’s formula to Analytic Signals; Character-ization of boundary values of functions in Hp Spaces on Tubes based on Regular cone; The exploration on weighted space of the right half plane.The outline of the article is arranged as follows:Chapter1present the basic notations,the background and main results.In chapter2, we use generalized Carleman’s formula to get some result on analytic signals, which is the generalization of Guan-Tie Deng, Tao Qian.In chapter3, we deal with Hp spaces on tubes, which can be divided into two parts: first, by constructing an analytic function on the tube, we state that its boundary limits don’t exist, this function is a generalization of the case n=2,P.95. Second, we give a characterization of boundary values of functions in Hp Spaces on Tubes based on Regular cone, the results generalize those obtained by T.Qian in the upper half-plane.In chapter4, we introduce the concept of weighted Hp spaces of the right half plane, and get the structure of weighted space by discussing the weighted function, and the relation with classical Hp spaces. Finally, we prove that a function in weighted space of the right half plane is uniquely determined by a sequence of positive real numbers with some conditions.