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Oscillatory hyper Hilbert transforms along variable curves |
Jiecheng CHEN1, Dashan FAN2, Meng WANG3() |
1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321001, China 2. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53301, USA 3. School of Mathematical Science, Zhejiang University, Hangzhou 310027, China |
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Abstract For n = 2 or 3 and , we study the oscillatory hyper Hilbert transformalong an appropriate variable curve in (namely, is a curve in for each fixed x), where . We obtain some boundedness theorems of , under some suitable conditions on and . These results are extensions of some earlier theorems. However, is not a convolution in general. Thus, we only can partially employ the Plancherel theorem, and we mainly use the orthogonality principle to prove our main theorems.
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Keywords
Hyper Hilbert transform
variable curve
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Corresponding Author(s):
Meng WANG
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Issue Date: 23 September 2019
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