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arXiv · 2105.03717

Boundedness of operators generated by fractional semigroups associated with Schr\"odinger operators on Campanato type spaces via $T1$ theorem

Zhiyong Wang·Pengtao Li·Chao Zhang
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Abstract

Let $\mathcal{L}=-\Delta+V$ be a Schr\"{o}dinger operator, where the nonnegative potential $V$ belongs to the reverse H\"{o}lder class $B_{q}$. By the aid of the subordinative formula, we estimate the regularities of the fractional heat semigroup, $\{e^{-t\mathcal{L}^{\alpha}}\}_{t>0},$ associated with $\mathcal{L}$. As an application, we obtain the $BMO^{\gamma}_{\mathcal{L}}$-boundedness of the maximal function, and the Littlewood-Paley $g$-functions associated with $\mathcal{L}$ via $T1$ theorem, respectively.

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Zhiyong Wang, Pengtao Li, Chao Zhang. 2021-05-08. Boundedness of operators generated by fractional semigroups associated with Schr\"odinger operators on Campanato type spaces via $T1$ theorem. https://arxiv.org/abs/2105.03717

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