Weak Boundedness for Littlewood-Paley g Functions on Weighted Herz Spaces

The weak boundedness on weighted Herz spaces is considered for Littlewood-Paley g functions.By the decomposition of weighted Herz space and several inequalities,it is obtained that gψ is boundedness from Kα,pq(ω1,ω2) to WKα,pq(ω1,ω2),then for ω1,ω2∈A1,when 0α≤n(1-1/q),and gψ is strong boundedness on weighted Herz spaces when 0αn(1-1/q).The result enriches the boundedness theory of Littlewood-Paley g functions.