Abstract
Let Γ be the set of all permutations of the natural series and let α = {α j} j∈ℕ, ν = {νj} j∈ℕ, and η = {ηj} j∈ℕ be nonnegative number sequences for which
is defined for all γ:= {γ(j)} j∈ℕ ∈ Γ and η ∈ l p. We find \(\sup _{\eta :\left\| \eta \right\|_p = 1} \inf _{\gamma \in \Gamma } \left\| {\nu (\alpha \eta )_\gamma } \right\|_1 \) in the case where 1 < p < ∞.
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A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).
A. L. Shydlich, “Best n-term approximations by Λ-methods in spaces S pϕ ,” in: Extremal Problems in the Theory of Functions and Related Questions [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2003), pp. 283–306.
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge (1934).
E. I. Radzievskaya and G. V. Radzievskii, “On one extremal problem for a seminorm on the space l 1 with a weight,” Ukr. Mat. Zh., 57, No. 7, 1002–1006 (2005).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1430–1434, October, 2005.
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Radzievskaya, E.I., Radzievskii, G.V. On one extremal problem for numerical series. Ukr Math J 57, 1674–1678 (2005). https://doi.org/10.1007/s11253-006-0022-8
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DOI: https://doi.org/10.1007/s11253-006-0022-8