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 Mat. Zametki, 2001, Volume 69, Issue 4, Pages 515–523 (Mi mz520)

This article is cited in 2 scientific papers (total in 2 papers)

Distinguishing Between Symmetric Spaces and $L^\infty$ by a Differential Basis

E. I. Berezhnoi, A. A. Perfil'ev

P. G. Demidov Yaroslavl State University

Abstract: One of the fundamental problems in the theory of differentiation of integrals is the following. Let $X$ and $Y$ be two spaces which are different in some sense. Does there exist a differential basis that differentiates the space $X$, i.e., all integrals of functions from $X$, but not integrals of functions from $Y$, i.e., there exists a function from $Y$ whose integral cannot be differentiated by this basis. In this paper we construct a basis which differentiates the space $L^\infty$ but does not differentiate any other symmetric space $X\ne L^\infty$.

DOI: https://doi.org/10.4213/mzm520

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English version:
Mathematical Notes, 2001, 69:4, 467–474

Bibliographic databases:

UDC: 517.5
Received: 28.02.1999

Citation: E. I. Berezhnoi, A. A. Perfil'ev, “Distinguishing Between Symmetric Spaces and $L^\infty$ by a Differential Basis”, Mat. Zametki, 69:4 (2001), 515–523; Math. Notes, 69:4 (2001), 467–474

Citation in format AMSBIB
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\paper Distinguishing Between Symmetric Spaces and $L^\infty$ by a Differential Basis
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This publication is cited in the following articles:
1. E. I. Berezhnoi, A. V. Novikov, “The halo problem in the theory of differentiation of integrals”, Izv. Math., 66:4 (2002), 659–681
2. E. I. Berezhnoǐ, “On compactness of maximal operators”, Siberian Math. J., 56:4 (2015), 593–600
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