Regularity of the generalized Poisson operator
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Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where the potential $V$ belongs to the reverse H\"{o}lder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator $P^{L}_{t,\sigma}$, $0<\sigma<1$, associated with $L$. We estimate the gradient and the time-fractional derivatives of the kernel of $P^{L}_{t,\sigma}$, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space $\mathcal{C}^{\gamma}_{L}(\mathbb{R}^{n})$ via $P^{L}_{t,\sigma}$.
Abstract
Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where the potential $V$ belongs to the reverse H\"{o}lder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator $P^{L}_{t,\sigma}$, $0<\sigma<1$, associated with $L$. We estimate the gradient and the time-fractional derivatives of the kernel of $P^{L}_{t,\sigma}$, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space $\mathcal{C}^{\gamma}_{L}(\mathbb{R}^{n})$ via $P^{L}_{t,\sigma}$.
참고문헌 (21)
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