Let (M, J, g, ω) be a complete Hermitian manifold of complex dimension n≥ 2. Let 1 ≤ p≤ n- 1 and assume that ωn-p is (∂+ ∂¯) -bounded. We prove that, if ψ is an L2 and d-closed (p, 0)-form on M, then ψ= 0. In particular, if M is compact, we derive that if the Aeppli class of ωn-p vanishes, then HBCp,0(M)=0. As a special case, if M admits a Gauduchon metric ω such that the Aeppli class of ωn-1 vanishes, then HBC1,0(M)=0.
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