Carleson embeddings and some classes of operators on weighted Bergman spaces

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A Volterra-type integration operator on Fock spaces (2012, unknown): “The boundedness and compactness, as well as some spectral properties (such as Schatten class membership) of Tg acting on various spaces of analytic functions of the unit disc D in C have been extensively investigated (see [2, 6] for Hardy spaces, [3, 5, 8, 17, 19] for weighted Bergman spaces, and [9”
Small weighted Bergman spaces (2015, methodology): “For several classes of weights, q-Carleson measures for Aω [21, 42, 46] have been described, in the triangular case p > q, by using an atomic decomposition theorem in the sense of standard Bergman spaces [55, Theorem 2.”
Weighted Bergman spaces induced by rapidly incresing weights (2012, background): “The membership of the integral operator Tg in the Schatten p-class Sp(H) has been characterized when H is either the Hardy spaceH(2) [10], the classical weighted Bergman space A(2)α [11], or the weighted Bergman space A 2 ω , where ω is a rapidly decreasing weight [64, 65] or a Bekollé-Bonami weight”