  In the paper, the transition probability density of 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.
