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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
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
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
Linking options:
https://www.mathnet.ru/eng/im393https://doi.org/10.1070/IM2002v066n04ABEH000393 https://www.mathnet.ru/eng/im/v66/i4/p3
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Abstract page: | 366 | Russian version PDF: | 202 | English version PDF: | 13 | References: | 37 | First page: | 1 |
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