The authors study the possibility to introduce functional calculus generated by the Laplacian corresponding to the multidimensional space with Gaussian measure. Though they prove, that the general result of \textit{S. Meda} [Proc. Am. Math. Soc. 110, No. 3, 639-647 (1990; Zbl 0760.42007)] cannot be applied to the case. They succeed in constructing the multipliers of Laplace transform type associated to the Laplacian. The boundednes on \(L^p\) for \(1\varepsilon} K(x,y)f(y)dy),\) for almost all \(x\), whenever \(f\) is a test function.