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arXiv · 2011.00465

Notes on lattice bump Fourier multiplier operators on $L^2 \times L^2$

Tomoya Kato·Akihiko Miyachi·Naohito Tomita
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Abstract

Given a smooth bump function, we consider the multiplier formed by taking the linear combination of the translations of the bump function and the corresponding bilinear Fourier multiplier operator. Under certain condition on the bump function, we give a complete characterization of the coefficients of the linear combination for which the corresponding bilinear operator defines a bounded operator from $L^2\times L^2$ to $L^2$-based amalgam spaces.

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Tomoya Kato, Akihiko Miyachi, Naohito Tomita. 2020-11-01. Notes on lattice bump Fourier multiplier operators on $L^2 \times L^2$. https://arxiv.org/abs/2011.00465

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