  We study multivariable spectral multipliers $F(L_1,L_2)$ acting on Cartesian
product of ambient spaces of two self-adjoint operators $L_1$ and $L_2$. We
prove that if $F$ satisfies H\"ormander type differentiability condition then
the operator $F(L_1,L_2)$ is of Calder\'on-Zygmund type. We apply obtained
results to the analysis of quasielliptic operators acting on product of some
fractal spaces. The existence and surprising properties of quasielliptic
operators have been recently observed in works of Bockelman, Drenning and
Strichartz. This paper demonstrates that Riesz type operators corresponding to
quasielliptic operators are continuous on $L^p$ spaces.
