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- W2055714810 abstract "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 0<p<1; moreover, it is a bounded operator from Hp(Rn) into Lp,∞(Rn). In addition, if ϱd∈C∞(Rn∖{0}), then we also prove that Gϱdδ is a bounded operator from Hp(Rn) into Lp(Rn) when δ>n(1/p−1/2)−1/2 and 0<p<1." @default.
- W2055714810 created "2016-06-24" @default.
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- W2055714810 date "2008-03-01" @default.
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- W2055714810 title "Weak type estimates of square functions associated with quasiradial Bochner–Riesz means on certain Hardy spaces" @default.
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- W2055714810 doi "https://doi.org/10.1016/j.jmaa.2007.06.050" @default.
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