Abstract
To obtain groups with bounded harmonic functions (which are amenable), one of the most frequent way is to look at some semi-direct products (e.g. lamplighter groups). The aim here is to show that many of these semi-direct products do not admit harmonic functions with gradient in ℓ p, for \(p\in [1,\infty [\).
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Gournay, A. Absence of Non-Constant Harmonic Functions with ℓ p-gradient in some Semi-Direct Products. Potential Anal 45, 109–117 (2016). https://doi.org/10.1007/s11118-016-9537-2
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DOI: https://doi.org/10.1007/s11118-016-9537-2