Oscillatory hyper Hilbert transforms along variable curves |
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Authors: | Jiecheng CHEN Dashan FAN Meng WANG |
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Institution: | 1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321001, China2. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53301, USA3. 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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