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arXiv · 1912.06233

Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

Akihiko Miyachi·Naoto Shida·Naohito Tomita
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Abstract

In this paper, the $L^2 \times L^{\infty} \to L^2$ and $L^2 \times L^2 \to L^1$ boundedness of bilinear Fourier multiplier operators is discussed under weak smoothness conditions on multipliers. As an application, we prove the $L^2 \times BMO \to L^2$ and $L^2 \times L^2 \to H^1$ boundedness of bilinear operators with multipliers of limited smoothness satisfying vanishing conditions.

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Akihiko Miyachi, Naoto Shida, Naohito Tomita. 2019-12-12. Limited smoothness conditions with mixed norms for bilinear Fourier multipliers. https://arxiv.org/abs/1912.06233

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