Reducibility And Unitary Equivalence For A Class Of Analytic Multipliers On Sobolev Disk Algebra

This thesis mainly study the reducibility,unitary equivalence and the number of reducing spaces for a class of analytic multipliers with N-Blaschke product symbol on Sobolev disk algebra.In Chapter 1,we give some related research background about the reducibility on some classical analytic function spaces,and some basic concepts and notations.At last,we present the main results of the research.In Chapter 2,we give the sufficient and necessary condition for the reducibility of analytic multiplier M? when ? is N-Blaschke product(N = 2,3,4).We completely characterize the reducibility of analytic multiplier M? when ? is 2-Blaschke product,and give partly results for the reducibility of analytic multiplier M? when ? is N-Blaschke product(N = 3,4).In Chapter 3,we prove that for a N-Blaschke product(N>1)?,when M? is unitary equivalent to MZN.