25 citations · 84 across the 16 of their papers we have counts for
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A Hörmander spectral multiplier theorem for fractional Hardy operators
Konstantin Merz
We consider the fractional Laplacian with added critical or subcritical Hardy potential, called Hardy operator. We prove a Hörmander spectral multiplier theorem, i.e., the boundedn…
On wave operators for Hardy operators with and without perturbations
Atsuhide Ishida, Konstantin Merz
We prove asymptotic completeness of the wave operators in time-dependent scattering theory which intertwine the ordinary or fractional Laplacian and the corresponding Hardy operato…
Subordinated Bessel heat kernels
Krzysztof Bogdan, Konstantin Merz
We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.
Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
Krzysztof Bogdan, Konstantin Merz
Motivated by the study of relativistic atoms, we consider the Hardy operator acting on functions of the form in $L^2(\m…
On Sobolev norms involving Hardy operators in a half-space
Rupert L. Frank, Konstantin Merz
We consider Hardy operators on the half-space, that is, ordinary and fractional Schrödinger operators with potentials given by the appropriate power of the distance to the boundary…
On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle
Konstantin Merz
We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a…
On Scales of Sobolev spaces associated to generalized Hardy operators
Konstantin Merz
We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous Sobolev spaces generated by this operator. Besides generalized and reversed Hardy…
Equivalence of Sobolev norms involving generalized Hardy operators
Rupert L. Frank, Konstantin Merz, Heinz Siedentop
We consider the fractional Schrödinger operator with Hardy potential and critical or subcritical coupling constant. This operator generates a natural scale of homogeneous Sobolev s…