2011
DOI: 10.1007/s11253-011-0567-z
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Sharp upper bounds of norms of functions and their derivatives on classes of functions with given comparison function

Abstract: For arbitrary OE˛;ˇ R and p > 0; we solve the extremal problem Z jx .k/ .t /j q dt ! sup; q p; k D 0 or q 1; k 1;on the set of functions S k ' such that ' .i / is a comparison function for x .i / ; i D 0; 1; : : ::In particular, we solve this extremal problem on Sobolev classes and on bounded subsets of the spaces of trigonometric polynomials and splines.

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Cited by 9 publications
(1 citation statement)
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“…By using Theorem 1 and the results obtained in [2], for any segment [↵, β] ⇢ R and given r 2 N, A, and h, p > 0, we solve the extremal problem…”
Section: Introductionmentioning
confidence: 99%
“…By using Theorem 1 and the results obtained in [2], for any segment [↵, β] ⇢ R and given r 2 N, A, and h, p > 0, we solve the extremal problem…”
Section: Introductionmentioning
confidence: 99%