Geodesic
The Composition Operator on Mixed-Norm Lebesgue Spaces
Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 816-823.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, measurable mappings.
Mots-clés : mixed-norm Lebesgue spaces 
@article{MZM_2019_105_6_a1,
     author = {N. A. Evseev and A. V. Menovshchikov},
     title = {The {Composition} {Operator} on {Mixed-Norm} {Lebesgue} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {816--823},
     publisher = {mathdoc},
     volume = {105},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a1/}
}
TY  - JOUR
AU  - N. A. Evseev
AU  - A. V. Menovshchikov
TI  - The Composition Operator on Mixed-Norm Lebesgue Spaces
JO  - Matematičeskie zametki
PY  - 2019
SP  - 816
EP  - 823
VL  - 105
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a1/
LA  - ru
ID  - MZM_2019_105_6_a1
ER  - 
%0 Journal Article
%A N. A. Evseev
%A A. V. Menovshchikov
%T The Composition Operator on Mixed-Norm Lebesgue Spaces
%J Matematičeskie zametki
%D 2019
%P 816-823
%V 105
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a1/
%G ru
%F MZM_2019_105_6_a1
N. A. Evseev; A. V. Menovshchikov. The Composition Operator on Mixed-Norm Lebesgue Spaces. Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 816-823. http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a1/

[1] R. K. Singh, J. S. Manhas, Composition Operators on Function Spaces, North-Holland Math. Stud., 179, North-Holland Publ., Amsterdam, 1993 | MR | Zbl

[2] S. K. Vodopyanov, A. D. Ukhlov, “Operatory superpozitsii v prostranstvakh Lebega i differentsiruemost kvaziadditivnykh funktsii mnozhestva”, Vladikavk. matem. zhurn., 4:1 (2002), 11–33 | MR | Zbl

[3] S. K. Vodopyanov, A. D. Ukhlov, “Funktsii mnozhestva i ikh prilozheniya v teorii prostranstv Lebega i Soboleva. I”, Matem. tr., 6:2 (2003), 14–65 | MR | Zbl

[4] S. K. Vodopyanov, N. A. Evseev, “Izomorfizmy sobolevskikh prostranstv na gruppakh Karno i metricheskie svoistva otobrazhenii”, Dokl. AN, 464:2 (2015), 131–135 | DOI | MR | Zbl

[5] N. A. Evseev, “Operatory kompozitsii v vesovykh prostranstvakh Soboleva na gruppe Karno”, Sib. matem. zhurn., 56:6 (2015), 1304–1325 | DOI | MR | Zbl

[6] N. A. Evseev, “Ogranichennyi operator kompozitsii na prostranstvakh Lorentsa”, Matem. zametki, 102:6 (2017), 836–843 | DOI | Zbl

[7] A. V. Menovschikov, “Operatory kompozitsii v prostranstvakh Soboleva–Orlicha”, Sib. matem. zhurn., 57:5 (2016), 1088–1101 | DOI

[8] S. Stević, “Weighted composition operators between mixed norm spaces and $\mathscr H^\infty_a$ spaces in the unit ball”, J. Inequal. Appl., 2007, Art. ID 28629 | MR

[9] S. Stevich, “Proizvedeniya operatorov integralnogo tipa i operatorov kompozitsii iz prostranstva so smeshannoi normoi v prostranstva tipa Blokha”, Sib. matem. zhurn., 50:4 (2009), 915–927 | MR

[10] N. Evseev, A. Menovschikov, “Bounded operators on mixed norm Lebesgue spaces”, Complex Anal. Oper. Theory, 2018 | DOI

[11] A. Benedek, R. Panzone, “The spaces $L^p$, with mixed norm”, Duke. Math. J., 28 (1961), 301–324 | DOI | MR | Zbl

[12] S. Berhanu, P. Cordaro, V. Hounie, An Introduction to Involutive Structures, Cambridge Univ. Press, Cambridge, 2008 | MR | Zbl

[13] O. V. Besov, “Otsenki proizvodnykh v smeshannoi $L_p$-norme na oblasti i rasprostranenie funktsii”, Matem. zametki, 7:2 (1970), 147–154 | MR | Zbl

[14] R. Haydon, M. Levy, Y. Raynaud, Randomly Normed Spaces, Hermann, Paris, 1991 | MR | Zbl

[15] P. Khalmosh, Teoriya mery, IL, M., 1953 | MR

[16] N. Evseev, A. Menovschikov, Mixed Operators on $L^p$-Direct Integrals, 2019, arXiv: 1902.02983