Kolmogorov-type inequalities for mixed derivatives of functions of many variables |
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Authors: | V F Babenko N P Korneichuk S A Pichugov |
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Institution: | (1) Dnepropetrovsk University, Dnepropetrovsk;(2) Institute for Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk;(3) Dnepropetrovsk Agricultural University, Dnepropetrovsk |
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Abstract: | Let = ( 1,..., d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that and for all
Moreover, if
is the least possible value of the exponent in this inequality, then
Deceased.Translated from Ukrains kyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 579–594, May, 2004. |
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Keywords: | |
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