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arXiv · 1101.4139

Multipliers of Laplace transform type in certain Dunkl and Laguerre settings

Tomasz Szarek
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Abstract

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 $L^p$, $1<p<\infty$, and from $L^1$ to weak $L^1$.

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Tomasz Szarek. 2011-01-21. Multipliers of Laplace transform type in certain Dunkl and Laguerre settings. https://arxiv.org/abs/1101.4139

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