Interpolation and embeddings of weighted tent spaces
Alex Amenta

TL;DR
This paper extends the theory of weighted tent spaces on metric measure spaces, identifying their interpolation spaces with new Z-spaces and establishing Hardy-Littlewood-Sobolev embeddings, advancing analysis in geometric and boundary value problems.
Contribution
It introduces Z-spaces as new interpolation spaces for weighted tent spaces on metric measure spaces, linking them to boundary value problem analysis.
Findings
Identification of interpolation spaces as Z-spaces
Establishment of Hardy-Littlewood-Sobolev embeddings
Extension of tent space theory to weighted and geometric settings
Abstract
Given a metric measure space , we consider a scale of function spaces , called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on we identify some associated interpolation spaces, in particular certain real interpolation spaces. These are identified with a new scale of function spaces, which we call -spaces, that have recently appeared in the work of Barton and Mayboroda on elliptic boundary value problems with boundary data in Besov spaces. We also prove Hardy--Littlewood--Sobolev-type embeddings between weighted tent spaces.
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