Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 3: 647 - 666

DOI: https://doi.org/10.1007/s11464-018-0688-x

RESEARCH ARTICLE

Oscillatory hyper-Hilbert transform along curves on modulation spaces

  • Xiaomei WU , 1 ,
  • Dashan FAN 2
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  • 1. Xingzhi College, Zhejiang Normal University, Jinhua 321004, China
  • 2. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA

Received date: 30 Oct 2017

Accepted date: 20 Jan 2018

Published date: 11 Jun 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We consider the boundedness of the n-dimension oscillatory hyper-Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems signicantly improve some known results.

Key words： Oscillatory hyper-Hilbert transform; inhomogeneous Besov spaces; -modulation spaces; homogeneous curves

Cite this article

Xiaomei WU , Dashan FAN . Oscillatory hyper-Hilbert transform along curves on modulation spaces[J]. Frontiers of Mathematics in China, 2018 , 13(3) : 647 -666 . DOI: 10.1007/s11464-018-0688-x

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