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In the paper, the transition probability density of isotropic $\alpha$-stablestochastic process in a finite dimensional Euclidean space is considered. Theresults of applying pseudo differential operators with respect spatialvariables 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. Thefirst operator with negative sign is fractional Laplacian and the second onemultiplied by imaginary unit is fractional gradient.

Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $\alpha$-stable stochastic process