Multivariable spectral multipliers and analysis of quasielliptic operators on fractals Adam Sikora 42B1543A8528A80spectral multipliersanalysis on fractals We study multivariable spectral multipliers $F(L_1,L_2)$ acting on the 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 products 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. This solves the problem posed in [B. Bockelman and R.S. Strichartz, \emph{Partial differential equations on products of Sierpin\'nski gaskets}, Indiana Univ. Math. J. \textbf{56} (2007), (1.3) p. 1363]. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3745 10.1512/iumj.2009.58.3745 en Indiana Univ. Math. J. 58 (2009) 317 - 334 state-of-the-art mathematics http://iumj.org/access/