Frontiers of Mathematics in China >
Double Hilbert transform on
Received date: 12 Aug 2011
Accepted date: 19 Nov 2012
Published date: 01 Aug 2013
Copyright
We introduce a space , where is the testing function space whose functions are infinitely differentiable and have bounded support, and is the space the double Hilbert transform acting on the testing function space.We prove that the double Hilbert transform is a homeomorphism from onto itself.
Key words: Double Hilbert transform; vanishing moments; homeomorphism
Xiaona CUI , Rui WANG , Dunyan YAN . Double Hilbert transform on [J]. Frontiers of Mathematics in China, 2013 , 8(4) : 783 -799 . DOI: 10.1007/s11464-013-0269-y
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