A restriction theorem for stable rank two vector bundles on P3

Let E be a normalized, rank two vector bundle on P3. Let H be a general plane. If E is stable with c2≥4, we show that h0(EH(1))≤2+c1. It follows that h0(E(1))≤2+c1. We also show that if E is properly semi-stable and indecomposable, h0(EH(1))=3.