Illinois Journal of Mathematics

On $L^{p}$-contractivity of Laguerre semigroups

Adam Nowak and Krzysztof Stempak

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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.

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Illinois J. Math., Volume 56, Number 2 (2012), 433-452.

First available in Project Euclid: 22 November 2013

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Zentralblatt MATH identifier

Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 47G10: Integral operators [See also 45P05]


Nowak, Adam; Stempak, Krzysztof. On $L^{p}$-contractivity of Laguerre semigroups. Illinois J. Math. 56 (2012), no. 2, 433--452. doi:10.1215/ijm/1385129958.

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