Multipliers of Laplace transform type in certain Dunkl and Laguerre settings

Details Multipliers of Laplace transform type in certain Dunkl and Laguerre settings Multipliers of Laplace transform type in certain Dunkl and Laguerre settings

2011-01-21

arxiv.org/abs/1101.4139v1

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

We investigate Laplace type and Laplace-Stieltjes type multipliers in the $d$-dimensional setting of the Dunkl harmonic oscillator with the associated group of reflections isomorphic to $\mathbb{Z}_2^d$ and in the related context of Laguerre function expansions of convolution type. We use Calder\'on-Zygmund theory to prove that these multiplier operators are bounded on weighted $L^p$, $1

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