The Laguerre calculus ; Estimates for powers of the sub-Laplacian ; Estimates for the spectrum projection operators of the sub-Laplacian ; The inverse of the operator square _{\alpha } = {\sum }^n_{j=1}({X^2_j} - {X^2_{j+n}}) - 2i{\alpha } ; The explicit solution of the bar {\partial } Neumann problem in a non-isotropic Siegel domain ; Injectivity of the Pompeiu transform in the isotropic H n ; Morera-type theorems for holomorphic mathcal H^p spaces in H n (I) ; Morera-type theorems for holomorphic mathcal H^p spaces in H n (II)