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The Capacitary John–Nirenberg Inequality Revisited

Year: 2025
Type: article
Abstract: In this paper, we establish maximal function estimates, Lebesgue differentiation theory, Calderón–Zygmund decompositions, and John–Nirenberg inequalities for translation invariant Hausdorff contents. We further identify a key structural component of these results – a packing condition satisfied by these Hausdorff contents which compensates for the non-linearity of the capacitary integrals. We prove that for any outer capacity, this packing condition is satisfied if and only if the capacity is equivalent to its induced Hausdorff content. Finally, we use this equivalence to extend the preceding theory to general outer capacities which are assumed to satisfy this packing condition.
DOI: 10.1515/acv-2025-0022
Institutions: National Taiwan Normal University, National Taiwan University, National Center for Theoretical Sciences, National Center for Theoretical Sciences, Mathematics Division, University of Milano-Bicocca, University of Pittsburgh
Language: English
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W4413813006
FWCI:
Cites: 35
Cited by:
Related to: 10