Hardy classes and related spaces of analytic functions in the unit circle, polydisc, and ball

On traces of holomorphic functions on the unit polyball

“…Let us note that for n = 1 traces of Bergman spaces were completely described previously in [3] and [11] (see also, for example, [12] and reference there). In this paper as in case of polydisk estimates for expanded Bergman projection (the operator of polarization) are playing a crucial role during all our proofs.…”

“…Let M be a unit ball and let K be a polyball (product of m balls) in all holomorphic functions in the polydisk was studied by many authors before (see [2], [3], [5], [8], [9], [11], [12] and references there).…”

On Traces in Hardy Type Analytic Spaces in Bounded Strictly Pseudoconvex Domains and in Tubular Domains over Symmetric Cones

“…This trace problem in Hardy spaces(diagonal map problem) in the unit disk and in the unit polydisk was considered by many authors during last several decades. In polydisk some estimates related with this problem can be seen, for example, in [1,2]. In polydisk, but in particular values of parameters in [3] and in some papers from list of references of [1,2].…”

“…Then we define new mixed norm Hardy type classes in tubular domains and pseudoconvex domains (see [1,2] for much simpler case of the unit polydisk). Then we provide a complete proof of our assertion in polyball and then provide assertions in bounded pseudoconvex domains with smooth boundary and in tubular domains over symmetric cones.…”

“…In polydisk some estimates related with this problem can be seen, for example, in [1,2]. In polydisk, but in particular values of parameters in [3] and in some papers from list of references of [1,2]. A rather long history related with these type estimates of traces of Hardy spaces can be read in [4] and in [2] also.…”