Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener
Commentationes Mathematicae, Tome 50 (2010) no. 1.

Voir la notice de l'article dans European Digital Mathematics Library

Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener ϕ -variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.
Mots-clés : $$-variation in the Wiener sense, composition operator, uniformly continuous operator, left-left regularization, Jensen equation 
@article{COMA_2010__50_1_291532,
     author = {J. A. Guerrero and J. Matkowski and N. Merentes},
     title = {Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of {Wiener}},
     journal = {Commentationes Mathematicae},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/COMA_2010__50_1_291532/}
}
TY  - JOUR
AU  - J. A. Guerrero
AU  - J. Matkowski
AU  - N. Merentes
TI  - Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener
JO  - Commentationes Mathematicae
PY  - 2010
VL  - 50
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/COMA_2010__50_1_291532/
LA  - en
ID  - COMA_2010__50_1_291532
ER  - 
%0 Journal Article
%A J. A. Guerrero
%A J. Matkowski
%A N. Merentes
%T Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener
%J Commentationes Mathematicae
%D 2010
%V 50
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/COMA_2010__50_1_291532/
%G en
%F COMA_2010__50_1_291532
J. A. Guerrero; J. Matkowski; N. Merentes. Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener. Commentationes Mathematicae, Tome 50 (2010) no. 1. https://geodesic-test.mathdoc.fr/item/COMA_2010__50_1_291532/