Let $\mathcal{S}(\mathbb{R})$ be the Schwartz space, $H^{s}(\mathbb{R})$ be the fractional Sobolev for $s\in\mathbb{R}$ and let $\widehat{\psi}\in\mathcal{S}(\mathbb{R})$ supported on annulus ${2^{j-1}\leq\vert\xi\vert\leq 2^{j+1}}$. Let $\Vert \psi(2^{-j}\xi)\sigma(\xi)\Vert_{H^{s}}<\infty$ for $s>1/2$ and $j\in\mathbb{Z}$ and let $\widehat{T_{\sigma}f}(\xi)=\sigma({\xi})\widehat{f}(\xi)$. Is it true that $T_{\sigma}$ is bounded from $L^{\infty}(\mathbb{R})$ to $BMO(\mathbb{R})$ space?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
0
1
|
|
|
|
