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Oscillatory hyper Hilbert transforms along curves

Authors:

Institution:

[1]Dept. of Math., Zhejiang University, Hangzhou 310027, China [2]Dept. of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

Abstract:

The hyper Hilbert transform

$ T_n f(x) = \int_{ - 1}^1 {f(x - \Gamma (t))e^{ - i\|t\|^{ - \beta } } \|t\|^{ - 1 - \alpha } dt} $ T_n f(x) = \int_{ - 1}^1 {f(x - \Gamma (t))e^{ - i\|t\|^{ - \beta } } \|t\|^{ - 1 - \alpha } dt}

Keywords:	hyper Hilbert transform curve
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