Weak type estimates of square functions associated with quasiradial Bochner-Riesz means on certain Hardy spaces

Let ϱd∈C∞(Rn∖{0}) be a non-radial homogeneous distance function of degree d∈N satisfying ϱd(tξ)=tdϱd(ξ). For f∈S(Rn), we define square functions Gϱdδf(x) associated with quasiradial Bochner-Riesz means Rϱd,tδf of index δ byGϱdδf(x)=(∫0∞|Rϱd,tδ+1f(x)−Rϱd,tδf(x)|2dtt)1/2 where Rϱd,tδf(x)=F−1[(1−ϱd/td)+δfˆ](x). If {ξ∈Rn:ϱd(ξ)=1} is a smooth convex hypersurface of finite type, then we prove in an extremely easy way that Gϱdδ is well-defined on Hp(Rn) when δ=n(1/p−1/2)−1/2 and 0n(1/p−1/2)−1/2 and 0