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Maximal operators of pseudo-differential operators with rough symbols
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万方数据
维普
Consider a pseudo-differential operator Taf(x)=∫Rn eix·ξa(x,ξ)(f)(ξ)dξwhere the symbol a is in the rough Hörmander class L∞Smρ with m ∈ R and ρ ∈[0,1].In this note,when 1 ≤ p ≤ 2,if m＜n(ρ-1)/p and a ∈ L∞Smρ,then for any f ∈ S(Rn)and x ∈ Rn,we prove that M(Taf)(x)≤ C(M(|f|p)(x))1/p where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.
万方数据
维普
