Compact Toeplitz Operators for Weighted Bergman Spaces on Bounded Symmetric Domains

摘要

Let W Ì mathbb Cd{Omega subset{mathbb C}^{d}} be an irreducible bounded symmetric domain of type (r, a, b) in its Harish–Chandra realization. We study Toeplitz operators Tn_g{T^{nu}_{g}} with symbol g acting on the standard weighted Bergman space H_n2{H_nu^2} over Ω with weight ν. Under some conditions on the weights ν and ν ₀ we show that there exists C(ν, ν ₀) > 0, such that the Berezin transform [(g)tilde]_n0{tilde{g}_{nu_{0}}} of g with respect to H2_n0{H^2_{nu_0}} satisfies: labele0||[(g)tilde]_n0||_¥ £ C(n,n₀)||Tn_g||,label{e0}|tilde{g}_{nu_0}|_infty leq C(nu,nu_0)|T^nu_g|,