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

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Matematicheskie Zametki, 2015, Volume 98, Issue 6, Pages 907–922
DOI: https://doi.org/10.4213/mzm10725 (Mi mzm10725)

This article is cited in 10 scientific papers (total in 10 papers)

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

V. D. Stepanov^ab

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

Full-text PDF (556 kB) Citations (10)

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

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

Received: 16.04.2015

English version:
Mathematical Notes, 2015, Volume 98, Issue 6, Pages 957–970
DOI: https://doi.org/10.1134/S0001434615110280

Bibliographic databases:

Document Type: Article

UDC: 517.51

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/mzm10725

https://doi.org/10.4213/mzm10725

https://www.mathnet.ru/eng/mzm/v98/i6/p907

This publication is cited in the following 10 articles:

V. D. Stepanov, E. P. Ushakova, “Strong and weak associativity of weighted Sobolev spaces of the first order”, Russian Math. Surveys, 78:1 (2023), 165–202
V. D. Stepanov, “On Spaces Associated with Weighted Cesàro and Copson Spaces”, Math. Notes, 111:3 (2022), 470–477
Vladimir D. Stepanov, “On Cesàro and Copson type function spaces. Reflexivity”, Journal of Mathematical Analysis and Applications, 507:1 (2022), 125764
A. Gogatishvili, J. S. Neves, “Weighted norm inequalities for positive operators restricted on the cone of lambda-quasiconcave functions”, Proc. R. Soc. Edinb. Sect. A-Math., 150:1 (2020), 17–39
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
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line”, Russian Math. Surveys, 74:6 (2019), 1075–1115
I. V. Orlov, “The Method of Lagrange Multipliers for the Class of Subsmooth Mappings”, Math. Notes, 103:2 (2018), 323–327
I. V. Orlov, “Generalized Hamel basis and basis extension in convex cones and uniquely divisible semigroups”, Eurasian Math. J., 9:1 (2018), 69–82
I. V. Orlov, “Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone”, Math. Notes, 102:3 (2017), 361–368
D. V. Prokhorov, “On a Set Everywhere Dense in a Lebesgue Space on the Real Line”, Math. Notes, 100:4 (2016), 639–641

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	85
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