Kolmogorov inequalities for the norms of the Riesz derivatives of functions of many variables

Аннотация

New sharp Kolmogorov-type inequalities for the norms of the Riesz derivatives ∥D^αf∥_∞ of functions \( f\in {L}_{\infty, E}^{\nabla}\left({\mathrm{\mathbb{R}}}^m\right) \) are obtained. Some applications of obtained inequalities are investigated.