@article{Osypchuk_2023, title={Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $\alpha$-stable stochastic process}, volume={15}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/6521}, DOI={10.15330/cmp.15.2.381-387}, abstractNote={<p>In the paper, the transition probability density of an isotropic $\alpha$-stable stochastic process in a finite dimensional Euclidean space is considered. The results of applying pseudo-differential operators with respect spatial variables to this function are estimated from the both side: above and below. Operators in the consideration are defined by the symbols $|\lambda|^\varkappa$ and $\lambda|\lambda|^{\varkappa-1}$, where $\varkappa$ is some constant. The first operator with negative sign is fractional Laplacian and the second one multiplied by imaginary unit is fractional gradient.</p>}, number={2}, journal={Carpathian Mathematical Publications}, author={Osypchuk, M.M.}, year={2023}, month={Oct.}, pages={381–387} }