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Oscillatory hyper-Hilbert transform along curves on modulation spaces

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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.

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Acknowledgements

The authors are thankful to the referees for their careful reading and useful comments. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11501516, 11471288) and the Natural Science Foundation of Zhejiang Province (No. LQ15A010003).

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Authors and Affiliations

  1. Xingzhi College, Zhejiang Normal University, Jinhua, 321004, China

    Xiaomei Wu

  2. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA

    Dashan Fan

Authors
  1. Xiaomei Wu
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  2. Dashan Fan
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Correspondence to Xiaomei Wu.

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Wu, X., Fan, D. Oscillatory hyper-Hilbert transform along curves on modulation spaces. Front. Math. China 13, 647–666 (2018). https://doi.org/10.1007/s11464-018-0688-x

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

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