A Dominated Theorem on 5L(2, R) and Its Application

摘要

In this paper,we give the following dominated theorem:Let(φ(g)∈L^1(G∥K),φε（t）=1/εsht/ε/shtφ(t/ε),ε>0,and the least radical decreasing dominated function Φ(t)=sup|φ(y)|∈L^1(G∥K),If shtΦ(t) is monotonically decreasing on (0,∞）,then for any f ∈Lolc^1 (G∥K),the following inequality holds: supε>0|φε*f(x)|≤Cmf(x),where mf(x)is the Hardy-Littlewood maximal function of f ,and C=‖Φ‖1,An application of this dominated theorem is also given.