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A maximal function for families of Hilbert transforms along homogeneous curves
Mathematische Annalen ( IF 1.3 ) Pub Date : 2019-10-17 , DOI: 10.1007/s00208-019-01915-3
Shaoming Guo , Joris Roos , Andreas Seeger , Po-Lam Yung

Let $$H^{(u)}$$ H ( u ) be the Hilbert transform along the parabola $$(t, ut^2)$$ ( t , u t 2 ) where $$u\in \mathbb {R}$$ u ∈ R . For a set U of positive numbers consider the maximal function $${\mathcal {H}}^U \,f= \sup \{|H^{(u)}\, f|: u\in U\}$$ H U f = sup { | H ( u ) f | : u ∈ U } . We obtain an (essentially) optimal result for the $$L^p$$ L p operator norm of $${\mathcal {H}}^U$$ H U when $$2

中文翻译:

希尔伯特族沿齐次曲线变换的极大函数

令 $$H^{(u)}$$ H ( u ) 为沿抛物线 $$(t, ut^2)$$ ( t , ut 2 ) 的希尔伯特变换,其中 $$u\in \mathbb {R }$$ u∈R。对于一组 U 的正数,考虑极大函数 $${\mathcal {H}}^U \,f= \sup \{|H^{(u)}\, f|: u\in U\}$ $ HU f = sup { | H ( u ) f | : u ∈ U } 。当 $$2 时,我们为 $${\mathcal {H}}^U$$ HU 的 $$L^p$$ L p 算子范数获得(本质上)最优结果
更新日期:2019-10-17
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