论文标题
尖锐的功能和加权$ l^{p} $估计伪差异操作员，符号一般霍曼德类
Sharp function and weighted $L^{p}$ estimates for pseudo-differential operators with symbols in general Hörmander classes
论文作者
论文摘要
本文的目的是证明不平等，并建立对pseudo-differential运算符的加权$ l^{p} $ spaces $ t_ {a} $由符号$ a \ in s^{m} _ {\ varrho，Δ $ 0 \leqΔ<1 $。 首先，我们证明，如果$ m \ leq-n（1- \ varrho）/2 $，则$ $（t_ {a} u）^{\ sharp}（x）\ sillsim m（| U |^{2}）其次，结果表明，如果$ 1 \ leq r \ leq2 $和$ m \ leq- \ frac {n} {r} {r}（1- \ varrho）$，那么对于任何$ω$ $ l^{p}_Ω$。此外，这些结果在$ m $的范围内很明显。
The purpose of this paper is to prove pointwise inequalities and to establish the boundedness on weighted $L^{p}$ spaces for pseudo-differential operators $T_{a}$ defined by the symbol $a\in S^{m}_{\varrho,δ}$ with $0\leq\varrho\leq1,$ $0\leqδ<1$. Firstly, we prove that if $m\leq-n(1-\varrho)/2$, then $$(T_{a}u)^{\sharp}(x)\lesssim M(|u|^{2})^{1/2}(x)$$ for all $x\in\mathbb{R}^{n}$ and all Schwartz function $u$. Secondly, it is shown that if $1\leq r\leq2$ and $m\leq-\frac{n}{r}(1-\varrho)$, then for any $ω$ belongs to the class of Muckenhoupt weights $A_{p/r}$ with $r<p<\infty$, these operators are bounded on $L^{p}_ω$. Moreover, these results are sharp on the bound of $m$.
