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# Analysis Seminar – Oscar Guzman, Departamento de Matematicas, Universidad Nacional de Colombia, Bogota, Colombia

## March 31 @ 3:30 pm - 4:30 pm

VARIABLE EXPONENT BOUNDED VARIATION SPACES IN THE RIESZ

SENSE

Abstract

This talk introduces Variable Exponent Bounded Variation Spaces in the Riesz Sense. We prove some embedding results and present a Riesz representation lemma in our setting [1]. Also it shows an application of the latter result by characterizing the global Lipschitz Nemytskii operator on the newly introduced spaces [2].

Keywords: Nemytskii operator, Riesz representation Theorem, Variable Lebesgue spaces, Banach algebra.

References

[1] Castillo, R. E., Guzmán, O. M., Rafeiro, H. (2016). Variable exponent bounded variation spaces in the Riesz sense. Nonlinear Analysis: Theory, Methods and Applications, 132, 173-182.

[2] Castillo, R. E., Guzmán, O. M., Rafeiro, H. (2017). Nemytskii Operator in Riesz-Bounded Variation Spaces with Variable Exponent. Mediterranean Journal of Mathematics, 14(1), 2.