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Izvestiya: Mathematics, 2002, Volume 66, Issue 4, Pages 659–681
DOI: https://doi.org/10.1070/IM2002v066n04ABEH000393 (Mi im393) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
English version PDF (251 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM2002v066n04ABEH000393
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 $p=1$.
Received: 07.05.2001
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2002, Volume 66, Issue 4, Pages 3–26
DOI: https://doi.org/10.4213/im393
Bibliographic databases:
UDC: 517.5
MSC: 46E30, 46B15, 42B25
Language: English
Original paper language: Russian
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/im393}
\crossref{https://doi.org/10.4213/im393}
\mathscinet{http://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748480711}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:366
    Russian version PDF:202
    English version PDF:13
    References:37
    First page:1
     
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