论文标题
$ \ mathbb {r}^d $上的指数重量相关的weyl pseudoDifferential cyculus
A Weyl pseudodifferential calculus associated with exponential weights on $\mathbb{R}^d$
论文作者
论文摘要
我们构建了一个量身定制的Weyl pseudoDifferential微积分，该微积分是针对在$ \ mathbb {r}^d $上进行加权的$ l^p $空间的界限，并带有$ \ exp（-dex（x）$的权重，$ c^$ c^2 $，该设置功能均与diricleich相关联。确定了$ l^p $上有限运算符的符号类，并分析了其属性。该理论用于计算相关操作员的$ H^\ infty $角度上的上限，并在某些情况下推论已知的最佳结果。最后，根据代数观点对符号类进行丰富和研究。
We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted $L^p$ spaces over $\mathbb{R}^d$ with weights of the form $\exp(-ϕ(x))$, for $ϕ$ a $C^2$ function, a setting in which the operator associated to the weighted Dirichlet form typically has only holomorphic functional calculus. A symbol class giving rise to bounded operators on $L^p$ is determined, and its properties analysed. This theory is used to calculate an upper bounded on the $H^\infty$ angle of relevant operators, and deduces known optimal results in some cases. Finally, the symbol class is enriched and studied under an algebraic viewpoint.
