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Unimodular multipliers on \(\alpha\)-modulation spaces: a revisit with new method

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Abstract

By a new method derived from Nicola–Primo–Tabacco in [J Pseudo-Differ Oper Appl 10:359–378 (2019)], we study the boundedness on \(\alpha\)-modulation spaces of unimodular multipliers with symbol \(\mathrm {e}^{\mathrm {i}\mu (\xi )}\). Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions.

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Acknowledgements

This work was partially supported by the National Natural Foundation of China (Nos. 11701112, 11671414, 11771388, 11601456) and Natural Science Foundation of Fujian Province (Nos. 2020J01267, 2020J01708, 2017J01723, 2018J01430).

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Authors and Affiliations

  1. School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, People’s Republic of China

    Guoping Zhao

  2. School of Science, Jimei University, Xiamen, 361021, People’s Republic of China

    Weichao Guo

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  1. Guoping Zhao
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  2. Weichao Guo
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Correspondence to Weichao Guo.

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Communicated by Joachim Toft.

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Zhao, G., Guo, W. Unimodular multipliers on \(\alpha\)-modulation spaces: a revisit with new method. Ann. Funct. Anal. 12, 1 (2021). https://doi.org/10.1007/s43034-020-00089-3

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  • DOI: https://doi.org/10.1007/s43034-020-00089-3

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