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On an inequality of Kolmogorov and Stein

Published online by Cambridge University Press:  17 April 2009

Ha Huy Bang
Institute of Mathematics, P.O. Box 61, 10000 Bo Ho, Hanoi, Vietnam
Hoang Mai Le
Thainguyen Pedagogic College, Thainguyen, Vietnam
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A.N. Kolmogorov showed that, if f, f′, …, f (n) are bounded continuous functions on ℝ, then when 0 < k < n. This result was extended by E.M. Stein to Lebesgue Lp-spaces and by H.H. Bang to Orlicz spaces. In this paper, the inequality is extended to more general function spaces.

Research Article
Copyright © Australian Mathematical Society 2000



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