We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe.
"Quasianalytic ultradifferentiability cannot be tested in lower dimensions." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 505 - 517, november 2019. https://doi.org/10.36045/bbms/1576206353