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Mat. Zametki, 2015, Volume 98, Issue 6, Pages 907–922 (Mi mz10725)  

This article is cited in 6 scientific papers (total in 6 papers)

On Optimal Banach Spaces Containing a Weight Cone of Monotone or Quasiconcave Functions

V. D. Stepanovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Peoples Friendship University of Russia, Moscow

Abstract: Optimal (minimal) Banach spaces containing given cones of monotone or quasiconcave functions on the semiaxis from weighted Lebesgue spaces are described. Exact formulas for the norm of the optimal space are presented. All cases of the summation parameter are studied.

Keywords: optimal (minimal) Banach space, cone of monotone functions, cone of quasiconcave functions, weighted Lebesgue space, Sinnamon's lemma.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02732
Ministry of Education and Science of the Russian Federation НШ-4479.2014.1


DOI: https://doi.org/10.4213/mzm10725

Full text: PDF file (556 kB)
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English version:
Mathematical Notes, 2015, 98:6, 957–970

Bibliographic databases:

UDC: 517.51
Received: 16.04.2015

Citation: V. D. Stepanov, “On Optimal Banach Spaces Containing a Weight Cone of Monotone or Quasiconcave Functions”, Mat. Zametki, 98:6 (2015), 907–922; Math. Notes, 98:6 (2015), 957–970

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Prokhorov, “On a Set Everywhere Dense in a Lebesgue Space on the Real Line”, Math. Notes, 100:4 (2016), 639–641  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. V. Orlov, “Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone”, Math. Notes, 102:3 (2017), 361–368  mathnet  crossref  crossref  mathscinet  isi  elib
    3. I. V. Orlov, “The Method of Lagrange Multipliers for the Class of Subsmooth Mappings”, Math. Notes, 103:2 (2018), 323–327  mathnet  crossref  crossref  isi  elib
    4. I. V. Orlov, “Generalized Hamel basis and basis extension in convex cones and uniquely divisible semigroups”, Eurasian Math. J., 9:1 (2018), 69–82  mathnet
    5. V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis”, Math. Notes, 105:1 (2019), 91–103  mathnet  crossref  crossref  mathscinet  isi  elib
    6. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Kharakterizatsiya funktsionalnykh prostranstv, assotsiirovannykh s vesovymi prostranstvami Soboleva pervogo poryadka na deistvitelnoi osi”, UMN, 74:6(450) (2019), 119–158  mathnet  crossref  mathscinet
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