TY  - JOUR
ID  - Aziz2010
LB  - Aziz2010
AU  - Aziz, Wadie
AU  - Giménez, José
AU  - Merentes, Nelson
AU  - Sánchez, José Luis
TI  - Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz
ST  - Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 3
SP  - 241
EP  - 248
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.3.241
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.3.241
AB  - In this paper we prove that if a Nemytskij composition operator, generated by a function of three variables in which the third variable is a function one, maps a suitable large subset of the space of functions of bounded total \(\varphi\)-bidimensional variation in the sense of Riesz, into another such space, and is uniformly continuous, then its generator is an affine function in the function variable. This extends some previous results in the one-dimensional setting.
KW  - \(\varphi\)-bidimensional variation
KW  - uniformly continuous
KW  - Nemytskij operator
SN  - 1232-9274
ER  -