Compound Poisson approximations in ${\mathrm{\ell }}_p$-norm for sums of weakly dependent vectors

The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is approximated by a multivariate compound Poisson distribution and by signed compound Poisson measure. The local and ${\mathrm{\ell }}_{\alpha }$-norms are used to obtain the error bounds. The Heinrich method is used for the proofs.