Riesz transforms and spectral multipliers of the Hodge–Laguerre operator

On R+d, endowed with the Laguerre probability measure μαμα, we define a Hodge–Laguerre operator Lα=δδ⁎+δ⁎δLα=δδ⁎+δ⁎δ acting on differential forms. Here δ   is the Laguerre exterior differentiation operator, defined as the classical exterior differential, except that the partial derivatives ∂xi∂xi are replaced by the ‘‘Laguerre derivatives’’ xi∂xi, and δ⁎δ⁎ is the adjoint of δ   with respect to inner product on forms defined by the Euclidean structure and the Laguerre measure μαμα. We prove dimension-free bounds on LpLp, 1