Abstract
We study several Laguerre semigroups appearing in the literature and find sharp ranges of type parameters for which these semigroups are contractive on all $L^{p}$ spaces, $1\le p\le\infty$. We also answer a similar question for Bessel semigroups, which in a sense are closely related to the Laguerre semigroups. A bit surprisingly, in some cases the ranges turn out to be disconnected sets.
Citation
Adam Nowak. Krzysztof Stempak. "On $L^{p}$-contractivity of Laguerre semigroups." Illinois J. Math. 56 (2) 433 - 452, Summer 2012. https://doi.org/10.1215/ijm/1385129958
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