Multipliers of Laplace transform type in certain Dunkl and Laguerre settings
Keywords:multiplier, Dunkl harmonic oscillator, generalized Hermite expansions, Laguerre expansions of convolution type, Calder\'on-Zygmund operator, A_p weight
AbstractWe 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 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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