Duality for outer $L^p$ spaces

Abstract: The theory of $L^p$ spaces for outer measures, or outer $L^p$ spaces, was developed by Do and Thiele to encode the proof of boundedness of certain multilinear operators in a streamlined argument. Accordingly to this purpose, the theory was developed in the direction of the real interpolation features of these spaces, while other questions remained untouched. For example, the outer $L^p$ spaces are defined by quasi-norms generalizing the classical mixed $L^p$ norms on sets with a Cartesian product structure. Therefore, it is natural to ask whether in arbitrary settings the outer $L^p$ quasi-norms are equivalent to norms. In this talk, we will answer this question, with a particular focus on certain settings on the upper half space $\R^d \times (0,\infty)$ related to the work of Do and Thiele.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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