Abstract
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 $$1<p<\infty $$ having a specific compactness property can always be factored through the corresponding Bochner space of 1-integrable functions. Some applications in the context of the Fourier type of Banach spaces are also given.
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