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Oscillatory hyper Hilbert transforms along curves

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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 R n is investigated, where β > α > 0. An L p boundedness theorem of T 4 is obtained, which is an extension of some earlier results of n = 2 and n = 3.

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Authors and Affiliations

  1. Dept. of Math., Zhejiang University, Hangzhou, 310027, China

    Jie-cheng Chen & Meng Wang

  2. Dept. of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, 53201, USA

    Da-shan Fan

Authors
  1. Jie-cheng Chen
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  2. Da-shan Fan
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  3. Meng Wang
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Additional information

Supported by the National Natural Science Foundation of China (10571156; 10701064); ZJNSF (RC97017); the Zijin Project of Zhejiang University

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Chen, Jc., Fan, Ds. & Wang, M. Oscillatory hyper Hilbert transforms along curves. Appl. Math. J. Chin. Univ. 24, 336–342 (2009). https://doi.org/10.1007/s11766-009-1965-y

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  • DOI: https://doi.org/10.1007/s11766-009-1965-y

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