Maximal Factorization of Operators Acting in Kothe-Bochner Spaces

[EN] Using some representation results for Kothe-Bochner spaces of vector valued functions by means of vector measures, we analyze the maximal extension for some classes of linear operators acting in these spaces. A factorization result is provided, and a specific representation of the biggest vector valued function space to which the operator can be extended is given. Thus, we present a generalization of the optimal domain theorem for some types of operators on Banach function spaces involving domination inequalities and compactness. In particular, we show that an operator acting in Bochner spaces of p-integrable functions for any 1
First author is supported by Grant MTM2011-23164 of the Ministerio de Economia y Competitividad (Spain). Second author is supported by Grant 284110 of CONACyT (Mexico). Fourth author is supported by Grant MTM2016-77054-C2-1-P of the Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigaciones (Spain) and FEDER.