论文标题
傅立叶积分运算符上耐边空间上的粗糙假差异操作员
Rough pseudodifferential operators on Hardy spaces for Fourier integral operators
论文作者
论文摘要
我们证明了假数分支运算符的映射属性，该属性在Hardy空间上用于傅立叶积分运算符上的粗糙符号。符号$ a（x，η）$是$ c^{r} _ {*} s^{m} _ {1，δ} $类的元素，在$ x $ varible中有限的规律性有限。我们表明，关联的pseudoDifferential operator $ a（x，d）$映射sobolev spaces $ \ mathcal {h}^{s，p}，p} _ {fio}（\ mathbb {r}^n}）$ $ \ MATHCAL {H}^{我们的主要结果意味着，对于$ m = 0 $，$δ= 1/2 $和$ r> n-1 $，$ a（x，d）$在$ \ mathcal {h}^{p}^{p} _ {fio} _ {fio}（\ Mathbb {r}
We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,η)$ are elements of $C^{r}_{*}S^{m}_{1,δ}$ classes that have limited regularity in the $x$ variable. We show that the associated pseudodifferential operator $a(x,D)$ maps between Sobolev spaces $\mathcal{H}^{s,p}_{FIO}(\mathbb{R}^{n})$ and $\mathcal{H}^{t,p}_{FIO}(\mathbb{R}^{n})$ over the Hardy space for Fourier integral operators $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$. Our main result implies that for $m=0$, $δ=1/2$ and $r>n-1$, $a(x,D)$ acts boundedly on $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for all $p\in(1,\infty)$.
