Title: Hybrid Normed Ideal Perturbations of n-tuples of Operators I,
Abstract: In hybrid normed ideal perturbations of $n$-tuples of operators, the normed
ideal is allowed to vary with the component operators. We begin extending to
this setting the machinery we developed for normed ideal perturbations based on
the modulus of quasicentral approximation and an adaptation of our
non-commutative generalization of the Weyl--von~Neumann theorem. For commuting
$n$-tuples of hermitian operators, the modulus of quasicentral approximation
remains essentially the same when $\cC_n^-$ is replaced by a hybrid $n$-tuple
$\cC_{p_1,\dots}^-,\dots,\cC^-_{p_n}$, $p_1^{-1} + \dots + p_n^{-1} = 1$. The
proof involves singular integrals of mixed homogeneity.