Boyd indices and the Berger-Coburn phenomenon

We settle the issue of Berger-Coburn phenomenon on the Fock space completely for general symmetrically normed ideals C_Φ[jls-end-space/], where Φ is not equivalent to Φ_∞[jls-end-space/]. We show that if the Boyd indices of C_Φ satisfy the condition 1<p_Φ≤q_Φ<∞[jls-end-space/], then for f∈L^∞(Cⁿ)[jls-end-space/], we have H_f∈C_Φ if and only if H_f¯∈C_Φ[jls-end-space/]. We further show that if either p_Φ=1 or q_Φ=∞[jls-end-space/], then there is an f∈L^∞(Cⁿ) such that H_f∈C_Φ while H_f¯∉C_Φ[jls-end-space/].