Decay estimates for Schr\"odinger heat semigroup with inverse square potential in Lorentz spaces

Kazuhiro Ishige; Yujiro Tateishi

Decay estimates for Schr\"odinger heat semigroup with inverse square potential in Lorentz spaces

Analysis of PDEs 2020-09-16 v1

Authors: Kazuhiro Ishige , Yujiro Tateishi

Abstract

Let $H:=-\Delta+V$ be a nonnegative Schr\"odinger operator on $L^2({\bf R}^N)$ , where $N\ge 2$ and $V$ is an inverse square potential. In this paper we obtain sharp decay estimates of the operator norms of $e^{-tH}$ and $\nabla e^{-tH}$ in Lorentz spaces.

Keywords

schrödinger operator inverse square potential heat semigroup decay estimates lorentz spaces

Cite

@article{arxiv.2009.07001,
  title  = {Decay estimates for Schr\"odinger heat semigroup with inverse square potential in Lorentz spaces},
  author = {Kazuhiro Ishige and Yujiro Tateishi},
  journal= {arXiv preprint arXiv:2009.07001},
  year   = {2020}
}

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