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| Weighted Compact Commutator of Bilinear FourierMultiplier Operator |
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Citation： |
Guoen HU.Weighted Compact Commutator of Bilinear FourierMultiplier Operator[J].Chinese Annals of Mathematics B,2017,38(3):795~814 |
| Page view： 4311
Net amount： 4246 |
Authors： |
Guoen HU; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11371370). |
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| Abstract： |
Let $T_{\sigma}$ be the bilinear Fourier multiplier operator with
associated multiplier $\sigma$ satisfying the Sobolev regularity
that $\sup\limits_{\kappa\in
\mathbb{Z}}\|\sigma_{\kappa}\|_{W^{s}(\mathbb{R}^{2n})}<\infty$ for
some $s\in (n, 2n]$. In this paper, it is proved that the commutator
generated by $T_{\sigma}$ and ${\rm CMO}(\mathbb{R}^n)$ functions is
a compact operator from $L^{p_1}(\mathbb{R}^n, w_1)\times
L^{p_2}(\mathbb{R}^n, w_2)$ to $L^p(\mathbb{R}^n, \nu_{\vec{w}})$
for appropriate indices $p_1, p_2, p\in (1, \infty)$ with
$\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and weights $w_1, w_2$
such that $\vec{w}=(w_1, w_2)\in
A_{\vec{p}/\vec{t}}(\mathbb{R}^{2n})$. |
Keywords： |
Bilinear Fourier multiplier, Commutator, Bi(sub)linear
maximal operator, Compact operator |
Classification： |
42B15, 47B07, 42B25 |
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