论文标题
加权抛物线运营商的Kato Square Root问题
The Kato square root problem for weighted parabolic operators
论文作者
论文摘要
我们提供了简化而直接的证据，证明了抛物线的抛物线量估计值，其椭圆形形式的椭圆形部分和系数可能以可测量的方式取决于空间和时间。该论点依赖于当今的经典减少，用于二次估计和Carleson型不平等。估计的确切组织与早期工作不同。特别是，尽管操作员具有非自主性，但我们几乎完全完全将空间和时间变量分开。因此，我们可以允许由空间$ a_2 $ - 加权决定的退化椭圆度，在这种情况下，该椭圆度在此之前尚未对其进行治疗。
We give a simplified and direct proof of the Kato square root estimate for parabolic operators with elliptic part in divergence form and coefficients possibly depending on space and time in a merely measurable way. The argument relies on the nowadays classical reduction to a quadratic estimate and a Carleson-type inequality. The precise organization of the estimates is different from earlier works. In particular, we succeed in separating space and time variables almost completely despite the non-autonomous character of the operator. Hence, we can allow for degenerate ellipticity dictated by a spatial $A_2$-weight, which has not been treated before in this context.
