Abstract. We obtain certain estimates for the reproducing kernels of large weighted Bergman spaces. Applications of these estimates to boundedness of the Bergman projection on L p (D, ω p/2 ), complex interpolation and duality of weighted Bergman spaces are given.
A full description of the membership in the Schatten ideal Sp(A 2 ω) for 0 < p < ∞ of Toeplitz operators acting on large weighted Bergman spaces is obtained.
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