Abstract：We intro duce the Sσ- function and g＊λ, σ- function in the hy perbolic Hardy space Hpσ(1 ≤p <∞), w hich are similarto the S- function and g＊λ- function in harmonic analy sis respectively .I t is proved that if f ∈ Hpσ, then Sσ(f)and g＊λ, σ(f)are both in Lp(1 ≤p<∞).
