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Mat. Zametki, 2019, Volume 105, Issue 6, Pages 816–823 (Mi mz11976)  

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

The Composition Operator on Mixed-Norm Lebesgue Spaces

N. A. Evseevabc, A. V. Menovshchikovcb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c Peoples' Friendship University of Russia, Moscow

Abstract: It is known that the boundedness of the composition operator on Lebesgue spaces is equivalent to the integrability of the volume derivative of the measurable mapping inducing the given operator. In the present paper, we prove a similar result for mixed-norm Lebesgue spaces in the class of mappings preserving the priority of the variables.

Keywords: composition operator, mixed-norm Lebesgue spaces, measurable mappings.

Funding Agency Grant Number
Russian Science Foundation 16-41-02004
This work was carried out at RUDN University and supported by the Russian Science Foundation under grant 16-41-02004.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11976

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English version:
Mathematical Notes, 2019, 105:6, 812–817

Bibliographic databases:

UDC: 517
Received: 21.02.2018
Revised: 17.06.2018

Citation: N. A. Evseev, A. V. Menovshchikov, “The Composition Operator on Mixed-Norm Lebesgue Spaces”, Mat. Zametki, 105:6 (2019), 816–823; Math. Notes, 105:6 (2019), 812–817

Citation in format AMSBIB
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\paper The Composition Operator on Mixed-Norm Lebesgue Spaces
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 6
\pages 816--823
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\crossref{https://doi.org/10.4213/mzm11976}
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\transl
\jour Math. Notes
\yr 2019
\vol 105
\issue 6
\pages 812--817
\crossref{https://doi.org/10.1134/S0001434619050195}
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  • https://doi.org/10.4213/mzm11976
  • http://mi.mathnet.ru/eng/mz/v105/i6/p816

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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. N. A. Evseev, A. V. Menovschikov, “O zamene peremennykh v $L^p$-prostranstvakh s izmenyayuscheisya vnutrennei strukturoi”, Izv. vuzov. Matem., 2020, no. 3, 92–97  mathnet  crossref
  • Математические заметки Mathematical Notes
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