Abstract
In this article, we study the multilinear localization operator L φ, ψ F f associated to quaternion Fourier transform(QFT). If F satisfies some conditions, we prove this kind of multilinear operator is bounded on \(L^{2}(\mathbb{R}^{2}; \mathbb{H}) \times L^{2}(\mathbb{R}^{2}; \mathbb{H}) \times L^{2}(\mathbb{R}^{2}; \mathbb{H})\). Further more, if we fix F and φ, then L φ, ψ F f is a bilinear compact operator.
Corresponding author, supported by Natural Science Foundation of China (Grant No. 11471040) and the Fundamental Research Funds for the Central Universities (2014KJJCA10).
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Ma, G., Zhao, J. (2017). Multilinear Localization Operators Associated to Quaternion Fourier Transforms. In: Wong, M., Zhu, H. (eds) Pseudo-Differential Operators: Groups, Geometry and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47512-7_5
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DOI: https://doi.org/10.1007/978-3-319-47512-7_5
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