H(φ)空间的极大函数刻画

Maximal function description of H(φ)spaces

研究了模函数φ的上,下指标β_φ,α_φ的性质.证明了当α_φ>β_φ/(1+β_φ)时,H(φ)空间具有非切向、径向、弱型非切向和弱型径向极大函数特征,从而对 H(φ)空间完全建立了类似于经典 H^p 空间的特征刻画理论.

The propcrty of upper index β_φ and lower index α_φ for the modular function φ is studied.It has been proved that when α_φ>β_φ/(1+β_φ),H(φ)spaces has nontangential, vertical,weak nontangential and weak vertical maximal characterization,thcrcfore,the theory of Maximal characterization description alalogous to H^P(0<p≤1)spaces for H(φ)spaces is completely builded.