Invariant Subspace Of The Weighted Hardy Space

In this thesis we mainly give the construction of the invariant subspace of the multiplier algebra of weighted Hardy space H~2 (β) when it has finite number of zeros inthe unit disk under the condition that the weighted sequence satisfies:(?)(?)<+∞. We also discuss the boundness and essential normality of M_z on the weighted Hardy space.We can obtain the structure of the invariant subspace of the weighted Hardy space when it equals to its multiplier algebra.In chapter 1 ,we discuss some related research ground, and give some basic defini-tions and symbols. At last, we show the significance of the research work.In chapter 2,we introduce some basic definitions and properties of the weighted Hardy space.In chapter 3,we give the sufficient and necessary conditions of the boundness and essential normality of M_z on the weighted Hardy space.(1)M_z is bounded on the weighted Hardy space H~2 (β) if and only if sup (?)< +∞.(2)M_z is essentially normal on the weighted Hardy space if and only ifIn chapter 4, we characterize the construction of the invariant subspace M of the multiplier algebra M(H~2(β)) of the weighted Hardy space when the invariant subspace M has finite number of zeros in the unit disk under the condition that the weighted sequence satisfies:...