Almost Gorenstein Rees algebras of p_g-ideals, good ideals, and powers of the maximal ideals

Let (A,m) be a Cohen-Macaulay local ring, and let I be an ideal of A. We prove that the Rees algebra R(I) is an almost Gorenstein ring in the following cases: (1) (A, m) is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field K ≅ A/m, and I is a p_g-ideal; (2) (A, m) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and I =m^l for all l ≥ 1; (3) (A,m) is a regular local ring of dimension d ≥ 2, and I = m^d-1. Conversely, if R(m^l) is an almost Gorenstein graded ring for some l ≥ 2 and d ≥ 3, then l = d - 1.