Hardy—Littlewood定理的一个简单证明

A Simple Proof for the Theorem of Hardy-Littlewood

本文给出了Hardy-Littlewood定理的充分性的一个简单证明。

In this paper,we give a simple proof for the following theorem:Theorem[Hardy-Littlewood]if f(Z)is an analytic function in the nnit disk,thenM_P(r,f)=O(1/(1-r)~β)iff M_P(r,f′)=O(1/(1-r)^(β+1))where0<p≤∞,β>0 andM_∞(r,f)=max|f(re^(iθ))|0≤θ≤2x