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Limited smoothness conditions with mixed norms for bilinear Fourier multipliers
Collectanea Mathematica ( IF 0.7 ) Pub Date : 2020-05-24 , DOI: 10.1007/s13348-020-00289-z
Akihiko Miyachi , Naoto Shida , Naohito Tomita

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



中文翻译:

双线性傅立叶乘法器的具有混合范数的有限平滑条件

在本文中,双线性傅立叶乘子算子的\(L ^ 2 \ times L ^ {\ infty} \ rightarrow L ^ 2 \)\(L ^ 2 \ times L ^ 2 \ rightarrow L ^ 1 \)的估计是在弱平滑条件下对乘数进行了讨论。作为一个应用,我们证明了双线性算子的\(L ^ 2 \ times BMO \ rightarrow L ^ 2 \)\(L ^ 2 \ times L ^ 2 \ rightarrow H ^ 1 \)有界且有限光滑度的乘积满足消失的条件。

更新日期:2020-05-24
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