Preduals of metric BV spaces
Enrico Pasqualetto

TL;DR
This paper constructs explicit preduals for p-integrable BV spaces over metric measure spaces and shows the existence of a predual for the classical BV space in PI spaces, advancing the functional analysis of BV functions.
Contribution
It provides the first explicit construction of preduals for p-BV spaces and establishes the existence of a predual for BV spaces in PI spaces, extending the theory to extended metric-topological measure spaces.
Findings
Constructed isometric preduals for ${ m BV}_p({ m X})$ spaces.
Proved the existence of a predual for ${ m BV}({ m X})$ in PI spaces.
Developed foundational theory of BV functions in extended metric-topological measure spaces.
Abstract
We study the predual of the space of functions of bounded variation defined over a metric measure space with finite. More specifically, for any exponent we construct an isometric predual of the space of -integrable functions of bounded variation, which we equip with the norm . Moreover, we prove that the standard BV space , which fails to have a predual for some choices of the metric measure space, does have a predual in the case where is a PI space (i.e. a doubling metric measure space supporting a weak -Poincar\'{e} inequality) of finite diameter. Along the way, we also develop a basic theory of BV functions in the setting of extended metric-topological…
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Geometric Analysis and Curvature Flows
