Author

E. Ouhabaz

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Preprint Oct 2026

${\mathcal R}$-boundedness of Riesz transforms and spectral multipliers of Schr\"odinger operators

Let $\LL = -\Delta + V$ be a Schr\"odinger operator with a non-negative potential. It is known that its associated Riesz transform $\nabla \LL^{-\sfrac{1}{2}}$ is bounded on $L^p(\RR^d)$ for $p \in (1,2]$, with a bound independent of $V$. We prove more, namely that the set \[ \{ \nabla \LL^{-\sfrac{1}{2}},\ 0 \le V \in...

E. Ouhabaz · 0 citations

Preprint Oct 2026

Weak type $(1,1)$ estimates for Riesz transforms of elliptic operators and magnetic Schr\"odinger operators

Let $M$ be a complete Riemannian manifold and define a magnetic Schr\"odinger operator $\LL = ({\bf d}+ iA)^*({\bf d}+iA) + V$ where $A$ is a real $1$-differential form in $L^2_{loc}$ and $V \in L^1_{loc}$ is a nonnegative electric potential. We prove that the magnetic Riesz transform $({\bf d} + iA) \LL^{-\einhalb}$ i...

E. Ouhabaz · 0 citations