On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to Z 2 n (also negative values of the multiplicity function are admitted). Our investigations include maximal operators, g-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace–Stieltjes transform type. Using the general Calderón–Zygmund theory we prove that these objects are bounded in weighted L p spaces, 1 < p < ∞ , and from L 1 into weak L 1 .