RESEARCH ARTICLE

Double Hilbert transform on D(2)

  • Xiaona CUI 1 ,
  • Rui WANG 2 ,
  • Dunyan YAN , 1
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  • 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 2. School of Mathematics, Jilin University, Changchun 130012, China

Received date: 12 Aug 2011

Accepted date: 19 Nov 2012

Published date: 01 Aug 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We introduce a space DHH=D(2)H2H1D(2), where D(2) is the testing function space whose functions are infinitely differentiable and have bounded support, and H2H1D(2) is the space the double Hilbert transform acting on the testing function space.We prove that the double Hilbert transform is a homeomorphism from DHH onto itself.

Cite this article

Xiaona CUI , Rui WANG , Dunyan YAN . Double Hilbert transform on D(2)[J]. Frontiers of Mathematics in China, 2013 , 8(4) : 783 -799 . DOI: 10.1007/s11464-013-0269-y

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