Asymptotic behavior of eigenvalues of Toeplitz operators on the weighted analytic spaces

Essential Norms and Schatten(-Herz) Classes of Integration Operators from Bergman Spaces to Hardy Spaces

“…Then we have the following description of the membership in S h (A 2 α ) of Toeplitz operators, which was proved in [6] in the setting of weighted Bergman spaces A 2 ω on a domain Ω ⊂ C for some more general weights ω.…”

“…See [9] and references there for more details. Based on the work concerning Toeplitz operators in [6], our next result (see Theorem 5.4 in Section 5) gives a description of the decay of singular values of J b :…”

The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

“…The following proposition is proved by Chacón in [3] which is going to be employed in the proof of the compactness. Another application of Lemma 5.1 is on the decay of the eigenvalue of which is regarded as a generalization of Theorem 6.4 in [6]. .…”

“…Let be a compact operator and a continuous increasing function. The authors of [6] introduce the following class of operators on a Hilbert space . Say that if there is a positive constant 0 such that 1 where is the th singular value of .…”

“…Say that if there is a positive constant 0 such that 1 where is the th singular value of . To study the Schatten class of the Toeplitz operators on the Bergman spaces with Békollé-Bonami weights, we follows the strategy of [6]. The following Lemma is the generalized version of Theorem 6.2 in [6].…”