Trace ideal criteria for operators of Hankel type

Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains

“…and finally we recover the following (a different proof of this fact has been established, in a more general setting, by Beatrous and Li, see [8]). …”

Schatten Class Hankel Operators on the Harmonic Bergman Space of the Unit Ball

“…The main results are introduced in this section. We will also compare our results with those from [6] and [18]. Most of the necessary lemmas are given in Section 2, and the proof for the main results is given in Section 3.…”

“…Beatrous and Li [6] extend Theorem A from the unit ball to more general strictly pseudoconvex domains in C n . In fact they obtain a sufficient condition for commutators to be in S p for p ≥ 2 when the underlying domain can be identified as X × (0, ∞) via a diffeomorphism (assuming that X has a homogeneous structure).…”

“…Before introducing our main results, we should mention some related results from [6] and [18]. Let B 2n denote the unit ball in C n (i.e.…”

“…The unit ball B n is clearly such a domain. If the underlying domain is B n and if the kernel function is the reproducing kernel R(x, y) in Theorem 1.5 of [6], then their result becomes the following:…”