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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 4, Pages 3–26 (Mi izv393)  

This article is cited in 1 scientific paper (total in 1 paper)

The halo problem in the theory of differentiation of integrals

E. I. Berezhnoia, A. V. Novikovb

a P. G. Demidov Yaroslavl State University
b Institute for Physics of Microstructures, Russian Academy of Sciences

Abstract: Let there be given a Lorentz space and an Orlicz space with equal fundamental functions. We construct a differential basis that differentiates the integrals of functions belonging to the Lorentz space, but does not differentiate the integral of some function belonging to the Orlicz space. Such bases enable us to obtain a negative solution of the so-called halo problem for $p\in(1,\infty)$. Morillon [1], Russian p. 186, proved that this problem has a positive solution in the case when $p=1$.

DOI: https://doi.org/10.4213/im393

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English version:
Izvestiya: Mathematics, 2002, 66:4, 659–681

Bibliographic databases:

UDC: 517.5
MSC: 46E30, 46B15, 42B25
Received: 07.05.2001

Citation: E. I. Berezhnoi, A. V. Novikov, “The halo problem in the theory of differentiation of integrals”, Izv. RAN. Ser. Mat., 66:4 (2002), 3–26; Izv. Math., 66:4 (2002), 659–681

Citation in format AMSBIB
\Bibitem{BerNov02}
\by E.~I.~Berezhnoi, A.~V.~Novikov
\paper The halo problem in the theory of differentiation of integrals
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 4
\pages 3--26
\mathnet{http://mi.mathnet.ru/izv393}
\crossref{https://doi.org/10.4213/im393}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1942093}
\zmath{https://zbmath.org/?q=an:1030.46029}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 4
\pages 659--681
\crossref{https://doi.org/10.1070/IM2002v066n04ABEH000393}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748480711}


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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. E. I. Berezhnoǐ, “On compactness of maximal operators”, Siberian Math. J., 56:4 (2015), 593–600  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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