16 citations · 87 across the 36 of their papers we have counts for
42 papers
Sparse bounds for rough non-translation-invariant Calderón-Zygmund operators
Yanping Chen, Teng Wang
In this paper, we establish sparse bounds for singular integral operators with rough non-translation-invariant Calderón-Zygmund kernels. Our approach verifies the localized hypothe…
-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 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 criterion…
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…