论文标题
与Schrödinger操作员相关的分数热半群的规律性
Regularity of fractional heat semigroup associated with Schrödinger operators
论文作者
论文摘要
令$ l =-Δ+v $为Schrödinger运营商，潜在的$ V $属于反向Hölder类。通过下属公式，我们介绍了与$ {l} $相关的分数热量半群$ \ {e^{ - t {l}^α} \} _ {t> 0}，α> 0 $。借助加热方程的基本解决方案：$$ \ partial_ {t} u+l u = \ partial_ {t} t} u-Δu+vu = 0，$$我们估计梯度和时间段衍生物的分数热kernel $ k^{l} l} _ {l} _ {$ cd）该方法与傅立叶变换无关，可以应用于二阶差分算子，其热核满足高斯上限。作为一个应用程序，我们建立了Carleson测量campanato类型空间的表征$ bmo^γ_{l}（\ Mathbb {r}^{n}）$ via $ \ {e^{ - t {l} {l}^α}^α} \} \} \} \} _ {t> 0} $。
Let $L=-Δ+V$ be a Schrödinger operator, where the potential $V$ belongs to the reverse Hölder class. By the subordinative formula, we introduce the fractional heat semigroup $\{e^{-t{L}^α}\}_{t>0}, α>0$, associated with ${L}$. By the aid of the fundamental solution of the heat equation: $$\partial_{t}u+L u=\partial_{t}u -Δu+Vu=0,$$ we estimate the gradient and the time-fractional derivatives of the fractional heat kernel $K^{L}_{α,t}(\cdot, \cdot)$, respectively. This method is independent of the Fourier transform, and can be applied to the second order differential operators whose heat kernels satisfying Gaussian upper bounds. As an application, we establish a Carleson measure characterization of the Campanato type space $BMO^γ_{L}(\mathbb{R}^{n})$ via $\{e^{-t{L}^α}\}_{t>0}$.
