Kolmogorov-type inequalities for mixed derivatives of functions of many variables

Abstract

Let γ = ( γ 1 , … , γ d ) be a vector with positive components and let D γ be the corresponding mixed derivative (of order γ j with respect to the j th variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove thatT . Moreover, if β is the least possible value of the exponent β in this inequality, then

Comparison of exact constants in Kolmogorov-type inequalities for periodic and nonperiodic functions of many variables

“…Note that, for λ = 0, the exponents in inequalities (8) We now proceed to the proof of equality (12).…”