Oscillatory hyper Hilbert transforms along general curves
Oscillatory hyper Hilbert transforms along general curves
复制标题
沿一般曲线振荡超希尔伯特变换
DOI：
10.1007/s11464-016-0574-3
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发表时间：
2017
影响因子：
--
通讯作者：
Zhu Xiangrong
中科院分区：
文献类型：
--
作者：
Chen Jiecheng;Damtew Belay Mitiku;Zhu Xiangrong
We consider the oscillatory hyper Hilbert transformHγ,α,βf(x) = ∫0∞f(x- Γ(t))eit-βt-(1+α)dt; where Γ(t) = (t,γ(t)) in ℝ2is a general curve. Whenγis convex, we give a simple condition onγsuch thatHγ,α,βis bounded onL2whenβ> 3α,β> 0: As a corollary, under this condition, we obtain theLp-boundedness ofHγ,α,βwhen 2β/(2β- 3α) <p< 2β/(3α). When Γ is a general nonconvex curve, we give some more complicated conditions onγsuch thatHγ,α,βis bounded onL2: As an application, we construct a class of strictly convex curves along whichHγ,α,βis bounded onL2only ifβ> 2α> 0.
