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Keywords:
embedding theorem; minimal domain; pseudoconvex domain; Bergman-type space
embedding theorem; minimal domain; pseudoconvex domain; Bergman-type space
Summary:
We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in $\mathbb {C}^{n}.$ Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are heavily based on nice properties of the $r$-lattice. Some results of this paper can be also obtained in some unbounded domains, namely tubular domains over symmetric cones.
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