This paper concerns harmonic analysis of the Ornstein–Uhlenbeck operator L on the Euclidean space. We examine the method of decomposing a spectral multiplier $$\phi (L)$$ into three parts according to the notion of admissibility, which quantifies the doubling behaviour of the underlying Gaussian measure $$\gamma $$ . We prove that the above-mentioned admissible decomposition is bounded in $$L^p(\gamma )$$ for $$1 < p \le 2$$ in a certain sense involving the Gaussian conical square function. The proof relates admissibility with E. Nelson’s hypercontractivity theorem in a novel way.