Hardy-Littlewood Maximal Function Inequalities Of τ-measurable Operators In Noncommutative Weak Orlicz Space

This paper presents noncommutative weak Orlicz space norm,then we obtain relevantinequalities in noncommutative weak LP space. in the last,we present weak averageinequality of Hardy-Littlewood maximal function inequalities ofÏ„-measurable operatorsand inequality of noncommutative weak Orlicz space norm.The three inequalities are asbelow:(a) If 1 < p <∞,we have‖MT_i^α(T)‖L_P^ω≦A₀‖T_i^α‖L_P^ω,T_i^α∈L_P^ω(M),(i=0,1)(b)sup_t>0Φ(t)λ_t(MT(|T|))≤C_Φsupt>0Φ(t)_λt(|T|), for all T∈L_Φ^ω(M).(c)IfΦis a strictly convex moderate young function, 1 < qΦ< pΦ<∞,then there isa constant C_Φ> 0 such that‖MT(|T|)‖L_Φ^ω≤C_Φ‖T‖L_Φ^ω,T∈L_Φ^ω(M).