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 Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 43–61 (Mi tm3703)

Construction of an optimal envelope for a cone of nonnegative functions with monotonicity properties

E. G. Bakhtigareeva, M. L. Goldman

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We study the problem of constructing a minimal quasi-Banach ideal space containing a given cone of nonnegative functions with monotonicity properties. The construction employs nondegenerate operators. We present general results on constructing optimal envelopes consistent with an order relation and obtain specifications of these constructions for various cones and various order relations. We also address the issue of order covering and order equivalence of cones.

 Funding Agency Grant Number Russian Science Foundation 14-11-00443 This work is supported by the Russian Science Foundation under grant 14-11-00443.

DOI: https://doi.org/10.1134/S0371968516020035

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 37–55

Bibliographic databases:

UDC: 517.51

Citation: E. G. Bakhtigareeva, M. L. Goldman, “Construction of an optimal envelope for a cone of nonnegative functions with monotonicity properties”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 43–61; Proc. Steklov Inst. Math., 293 (2016), 37–55

Citation in format AMSBIB
\Bibitem{BakGol16} \by E.~G.~Bakhtigareeva, M.~L.~Goldman \paper Construction of an optimal envelope for a~cone of nonnegative functions with monotonicity properties \inbook Function spaces, approximation theory, and related problems of mathematical analysis \bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii \serial Tr. Mat. Inst. Steklova \yr 2016 \vol 293 \pages 43--61 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3703} \crossref{https://doi.org/10.1134/S0371968516020035} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628469} \elib{http://elibrary.ru/item.asp?id=26344468} \transl \jour Proc. Steklov Inst. Math. \yr 2016 \vol 293 \pages 37--55 \crossref{https://doi.org/10.1134/S0081543816040039} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380722200003} \elib{http://elibrary.ru/item.asp?id=27119603} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979978248} 

• http://mi.mathnet.ru/eng/tm3703
• https://doi.org/10.1134/S0371968516020035
• http://mi.mathnet.ru/eng/tm/v293/p43

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This publication is cited in the following articles:
1. N. A. Bokayev, M. L. Goldman, G. Zh. Karshygina, “Some integral estimates on the cones of functions with the monotonicity conditions”, Bull. Karaganda Univ. Math., 90:2 (2018), 80–87
2. N. A. Bokaev, M. L. Gol'dman, G. Zh. Karshygina, “Cones of Functions with Monotonicity Conditions for Generalized Bessel and Riesz Potentials”, Math. Notes, 104:3 (2018), 348–363
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