Limit theorems for linear random fields with innovations in the domain of attraction of a stable law

In this paper we study the convergence in distribution and local limit theorem for partial sums of linear random fields with i.i.d. innovations that have infinite second moment belong to domain attraction a stable law index $0<\alpha\leq2$ under condition are centered if $1<\alpha\leq2$ symmetric $\alpha=1$. We establish these two types theorems as long well-defined, coefficients either absolutely summable or not summable.