Boundedness of operators related to a degenerate Schrödinger semigroup

ELEONOR HARBOURE; OSCAR SALINAS; BEATRIZ VIVIANI

POTENTIAL ANALYSIS

SPRINGER

Lugar: Berlin; Año: 2022 vol. 57 p. 401 - 431

0926-2601

In this work we search for boundedness results for operators related to thesemigroup generated by the degenerate Schrödinger operator $\LL u =-\frac{1}{\omega}\,\, \text{div}\,\, A\cdot \nabla u +V u$, where $\omega$ is aweight, $A$ is a matrix depending on $x$ and satisfying $\lambda \,\,\omega(x)|\xi|^2 \leq A(x)\xi\cdot \xi \leq \Lambda \,\, \omega(x)|\xi|^2$ forsome positive constants $\lambda$, $\Lambda$ and all $x$, $\xi$ in$\mathbb{R}^d$, assuming further suitable properties on the weight $\omega$ andon the non-negative potential $V$. In particular, we analyze the behaviour of$T^\ast$, the maximal semigroup operator, $\LL^{-\alpha/2}$, the negativepowers of $\LL$, and the mixed operators $\LL^{-\alpha/2}V^{\sigma/2}$ with$0