Sharp L 2 boundedness of the oscillatory hyper-Hilbert transform along curves

Authors
Chen, Jie Cheng Fan, Da Shan Zhu, Xiang Rong
Citation
Chen, Jie Cheng et al., Sharp L 2 boundedness of the oscillatory hyper-Hilbert transform along curves, Acta mathematica Sinica. English series (Print) , 26(4), 2010, pp. 653-658
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
26
Issue
4
Year of publication
2010
Pages
653 - 658
Database
ACNP
SICI code
Abstract
Consider the oscillatory hyper-Hilbert transform Hn,.,.f(x)=.10f(x..(t))eit..t.1..dt along the curve .(t) = (t p1, t p2, ..., t p n), where . > . . 0 and 0 < p 1 < p 2 < ... < p n . We prove that H n,.,. is bounded on L 2 if and only if . . (n + 1).. Our work extends and improves some known results.