On the spacel ^P(β)

Abstract

Let$\{ \beta (n)\} _{n = 0}^\infty$ be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel ^P(β) of all power series$f(z) = \sum\limits_{n = 0}^\infty {\hat f(n)z^n }$ such that$\sum\limits_{n = 0}^\infty {|\hat f(n)|^p |\beta (n)|^p }$. We give a necessary and sufficient condition for a polynomial to be cyclic inl ^P(β) and a point to be bounded point evaluation onl ^P(β).