BMO‐Type Norms Related to the Perimeter of Sets |
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| Authors: | Luigi Ambrosio Jean Bourgain Haim Brezis Alessio Figalli |
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| Institution: | 1. Scuola Normale Superiore, Pisa, Italy;2. School of Mathematics Institute for Advanced Study, Princeton, NJ, USA;3. Rutgers University, Department of Mathematics Hill Center, Busch Campus, Piscataway, NJ, USA;4. Technion, Department of Mathematics, Haifa, Israel;5. The University of Texas at Austin, Mathematics Department, Austin, TX, USA |
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| Abstract: | In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc. |
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