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- W4288331010 abstract "Let $K$ be a locally compact hypergroup with a left invariant Haar measure. We show that the Liouville property and amenability are equivalent for $K$ when it is second countable. Suppose that $sigma$ is a non-degenerate probability measure on $K$, we show that there is no non-trivial $sigma$-harmonic function which is continuous and vanishing at infinity. Using this, we prove that the space $H_sigma^p(K)$ of all $sigma$-harmonic $L^p$-functions, is trivial for all $1leq p<infty$. Further, it is shown that $H_sigma^infty(K)$ contains only constant functions if and only if it is a subalgebra of $L^infty(K)$. In the case where $sigma$ is adapted and $K$ is compact, we show that $H_sigma^p(K)={mathbb C}1$ for all $1leq pleqinfty$." @default.
- W4288331010 created "2022-07-28" @default.
- W4288331010 creator A5036831687 @default.
- W4288331010 creator A5072150568 @default.
- W4288331010 date "2019-06-12" @default.
- W4288331010 modified "2023-09-23" @default.
- W4288331010 title "Amenability and harmonic $L^p$-functions on hypergroups" @default.
- W4288331010 doi "https://doi.org/10.48550/arxiv.1906.05124" @default.
- W4288331010 hasPublicationYear "2019" @default.
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