Green Function Estimate For Subordinate Censored Stable Processes

In the last twenty years,the research on the discontinuous Markov process of orbit has developed rapidly in the two aspects of theory and application,especially under the Brown movement and stable processes.It has been studied deeply by experts and scholars at home and abroad,and has obtained abundant research results.The sym-metric stabe processes have good properties in the Green function estimation,Martin boundary,and conditional theory.In this paper,our main purpose is to study the prop-erties of Green functions and Markov kernel for subordinate censored stable processes.For subordinate censored stable processes,we take the special stable subordinate to obtain the sharp two-side estimates for Green function and the upper and lower bounds of the Jumping density.By using the dual process of the subordinate censored stable processes,we prove the boundary properties of the Martin kernel.This paper S_tex-presses the stable subordinate process,Z^Dis a censored?-stable subordinate on D and D is a C^1,1open set.This paper studies the Green function of the subordinate censored?-stable process Y^Dand the upper and lower bounds of Jumping density are also es-timated.Then,sharp two-side estimates for Martin kernel of Y^Dis obtained by using the sharp two-side estimates for Green function.