论文标题
$ l^2 \ times l^2 \ times l^2 \ to l^{2/3} $ thirinear乘数运算符的界限
$L^2\times L^2\times L^2\to L^{2/3}$ boundedness for trilinear multiplier operator
论文作者
论文摘要
本文讨论了三连乘数运算符$ t_ {m}（f_1，f_2，f_3）$的界限，当乘数满足一定程度的平滑度，但没有衰减条件，并且是$ l^{q} $ - 可允许的范围为$ q $ $ q $。有限性用$ \ | m \ | _ {l^{q}} $的术语表示。特别是，\ begin {equation*} \ | t_ {m} \ | _ {l^2 \ times l^2 \ times l^2 \ to l^{2/3}} \ sillesim \ simsim \ | m \ | m \ | _ {l^{l^{q}}}}}}}^{q/3} {q/q/q/q/3}。
This paper discusses the boundedness of the trilinear multiplier operator $T_{m}(f_1,f_2,f_3)$, when the multiplier satisfies a certain degree of smoothness but with no decaying condition and is $L^{q}$-integrable with an admissible range of $q$. The boundedness is stated in the terms of $\|m\|_{L^{q}}$. In particular, \begin{equation*}\|T_{m}\|_{L^2\times L^2\times L^2\to L^{2/3}}\lesssim\|m\|_{L^{q}}^{q/3}.\end{equation*}
