Boundedness of Spherical Local Maximal Operator for Radial Functions in the Plane
Gang Shen · Journal of Zhejiang Education Institute · 2007
Spherical local maximal functionMlocf(x) =sup0t |x|/2∫Sn-1f(x-ty′)dσ(y′)isshownto be of strongtype(p,p),and of weaktype(1,1) onLrpad(R2).Andforf∈Lrpad(R2),limt→∫0Sn-1f(x-ty′)dσ(y′) =f(x)is shownto hold almost everywhere.