Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions

Let be the space of bounded and continuous functions equipped with the norm and let e j , j = 1,…, m , be a standard basis in : Given moduli of continuity ω j , j = 1,…, m , denote We obtain new sharp Kolmogorov-type inequalities for the norms of mixed fractional derivatives of functions . Some applications of these inequalities are presented.