4 papers
math.FA2026
A weak type criterion for operators, and applications
Bernhard H. Haak, El-Maati Ouhabaz
Let be a space of homogeneous type and an open subset of . Given a bounded operator for some , we give a crite…
math.AP2025
Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem
Michel Bonnefont, El Maati Ouhabaz
On a fairly general class of Riemannian manifolds M, we prove lower estimates in terms of the Ricci curvature for the spectral bound (when M has infinite volume) and for the spectr…
math.AP2025
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…
math.AP2024
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\| Î^{\frac{1}{2} + ε} f \|_{p}\| Î^{\frac{1}…