Oscillatory hyper Hilbert transforms along curves

  • Jie-cheng Chen
  • Da-shan Fan
  • Meng Wang
Article

DOI: 10.1007/s11766-009-1965-y

Cite this article as:
Chen, J., Fan, D. & Wang, M. Appl. Math. J. Chin. Univ. (2009) 24: 336. doi:10.1007/s11766-009-1965-y
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Abstract

The hyper Hilbert transform
$$ T_n f(x) = \int_{ - 1}^1 {f(x - \Gamma (t))e^{ - i|t|^{ - \beta } } |t|^{ - 1 - \alpha } dt} $$
along an appropriate curve Γ(t) on Rn is investigated, where β > α > 0. An Lp boundedness theorem of T4 is obtained, which is an extension of some earlier results of n = 2 and n = 3.

Keywords

hyper Hilbert transform curve 

MR Subject Classification

42B25 

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Jie-cheng Chen
    • 1
  • Da-shan Fan
    • 2
  • Meng Wang
    • 1
  1. 1.Dept. of Math.Zhejiang UniversityHangzhouChina
  2. 2.Dept. of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA