Hardy Space On A Half - Band Region

Hardy space Hαp on a half strip consists of the functions analytic in the area Iαp={z=x+iy:x>0,|y|<α},and the norm‖·‖Hαp<∞.This article points out the functions in Hαp on a half strip have the following properties:(1)The function f has non-tangential limits,a.e.f*(t+iα),f*(t-iα)and f*(is).Moreover,the non-tangential limits are all in Lp(R)(2)The function f has a function class decomposition theorem；That is to say,for any f∈Hαp,z∈Iα,f(z)=B(z)g(z),B(z)consists of Blaschke product defined by the zero points of f(z),g(z)≠0,g∈Hαp,and‖g‖Hαp=‖f‖Hαp·(3)The function f has a Poisson integral representation；namely,for any f∈Hαp,f(z)is the poisson integral of its non-tangential boundary f*(t+iα), f*(t-iα)and f*(is).Further more,we give one necessary and suffcient condition that the func-tion F in the space Hαp,the norm equivalence of the two spaces Ep[α]and Hαp, and two theorems about the rational function on a half strip.