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- W1640902750 abstract "The $$L^1$$ -Sobolev inequality states that for compactly supported functions u on the Euclidean n-space, the $$L^{n/(n-1)}$$ -norm of a compactly supported function is controlled by the $$L^1$$ -norm of its gradient. The generalization to differential forms (due to Lanzani and Stein and Bourgain and Brezis) is recent, and states that a the $$L^{n/(n-1)}$$ -norm of a compactly supported differential h-form is controlled by the $$L^1$$ -norm of its exterior differential du and its exterior codifferential $$delta u$$ (in special cases the $$L^1$$ -norm must be replaced by the $$mathcal H^1$$ -Hardy norm). We shall extend this result to Heisenberg groups in the framework of an appropriate complex of differential forms." @default.
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- W1640902750 date "2015-11-30" @default.
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- W1640902750 title "Gagliardo-Nirenberg inequalities for differential forms in Heisenberg groups" @default.
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- W1640902750 doi "https://doi.org/10.1007/s00208-015-1337-2" @default.
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