16 citations · 87 across the 36 of their papers we have counts for
35 papers · 1 filter
-boundedness of Riesz transforms and spectral multipliers of Schrödinger operators
El Maati Ouhabaz
Let $\LL = -Δ+ V$ be a Schrödinger operator with a non-negative potential. It is known that its associated Riesz transform $\nabla \LL^{-\sfrac{1}{2}}$ is bounded on $L^p(\RR^d)$ f…
A multiplicative inequality of Riesz transform type on general Riemannian manifolds
El Maati Ouhabaz
Given any complete Riemannian manifold , we prove that for every and every , $$ \| \nabla f \|_p^2 \le C_ε\| Δ^{\frac{1}{2} + ε} f \|_{p}\| Δ^{\frac{1}{2} -…
Commutator estimates and Poisson bounds for Dirichlet-to-Neumann operators
A. F. M. ter Elst, E. M. Ouhabaz
We consider the Dirichlet-to-Neumann operator associated with a general elliptic operator \[ {\cal A} u = - \sum_{k,l=1}^d \partial_k (c_{kl}\, \partial_l u) + \sum_{k=1…
A simple construction of the Anderson operator via its quadratic form in dimensions two and three
Antoine Mouzard, El Maati Ouhabaz
We provide a simple construction of the Anderson operator in dimensions two and three. This is done through its quadratic form. We rely on an exponential transform instead of the r…
Fractional anisotropic Calderón problem on complete Riemannian manifolds
Mourad Choulli, El Maati Ouhabaz
We prove that the metric tensor of a complete Riemannian manifold is uniquely determined, up to isometry, from the knowledge of a local source-to-solution operator. This later…
Off-diagonal bounds for the Dirichlet-to-Neumann operator
Sebastian Bechtel, E. -M. Ouhabaz
Let be a bounded domain of with . We assume that the boundary of is Lipschitz. Consider the Dirichlet-to-Neumann operator associated w…