Frontiers of Mathematics in China >
Oscillatory hyper Hilbert transforms along variable curves
Received date: 08 Oct 2018
Accepted date: 30 Jul 2019
Published date: 15 Aug 2019
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For n = 2 or 3 and , we study the oscillatory hyper Hilbert transform
along 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.Key words: Hyper Hilbert transform; variable curve
Jiecheng CHEN , Dashan FAN , Meng WANG . Oscillatory hyper Hilbert transforms along variable curves[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 673 -692 . DOI: 10.1007/s11464-019-0783-7
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