8 citations · 22 across the 13 of their papers we have counts for
7 papers · 1 filter
Relativistic stable operators with critical potentials
Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
Non-symmetric Lévy-type operators
Jakub Minecki, Karol Szczypkowski
We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation $\partial_t =\mathca…
Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
Tomasz Jakubowski, Karol Szczypkowski
We investigate whether a fundamental solution of the Schrödinger equation has local in time sharp Gaussian estimates. We compare that class with the class…
Regularity of fundamental solutions for Lévy-type operators
Karol Szczypkowski
For a class of non-symmetric non-local Lévy-type operators , which include those of the form $$ \mathcal{L}^κf(x):= \int_{\mathbb{R}^d}( f(x+z)-f(x)- 1_{|z|<1} \left…
Fundamental solution for super-critical non-symmetric Lévy-type operators
Karol Szczypkowski
We prove the existence and give estimates of the fundamental solution (the heat kernel) for the equation for non-symmetric non-local operators $$ \mathc…
Heat kernels of non-symmetric Lévy-type operators
Tomasz Grzywny, Karol Szczypkowski
We construct the fundamental solution (the heat kernel) to the equation , where under certain assumptions the operator takes one of…
Gaussian estimates for Schroedinger perturbations
Krzysztof Bogdan, Karol Szczypkowski
We prove an optimal 4G Theorem for the Gaussian kernel. We also propose a new general method of estimating Schroedinger perturbations of transition densities, and give applications…