Graded pieces of Z^n-graded F-finite F-modules over K[[Y]][X1..Xn] are direct sums of E(A/YA), Q(A) and A with multiplicities constant on the sign blocks B(U).
Terai,Local cohomology modules with respect to monomial ideals, Proceedings of the 20th Symposium on Commutative Ring Theory (1998), 181-189
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On the structure theorem of graded components of $\mathcal{F}$-finite, $\mathcal{F}$-modules over certain polynomial ring
Graded pieces of Z^n-graded F-finite F-modules over K[[Y]][X1..Xn] are direct sums of E(A/YA), Q(A) and A with multiplicities constant on the sign blocks B(U).