On some new sharp embedding theorems in minimal and pseudoconvex domains

Romi F. Shamoyan; Olivera R. Mihić

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 527-546
  • ISSN: 0011-4642

Abstract

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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 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.

How to cite

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Shamoyan, Romi F., and Mihić, Olivera R.. "On some new sharp embedding theorems in minimal and pseudoconvex domains." Czechoslovak Mathematical Journal 66.2 (2016): 527-546. <http://eudml.org/doc/280089>.

@article{Shamoyan2016,
abstract = {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.},
author = {Shamoyan, Romi F., Mihić, Olivera R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {embedding theorem; minimal domain; pseudoconvex domain; Bergman-type space; Blaschke-type infinite canonical products; area Nevanlinna-type spaces; Nevanlinna characteristic; parametric representations; zero sets},
language = {eng},
number = {2},
pages = {527-546},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some new sharp embedding theorems in minimal and pseudoconvex domains},
url = {http://eudml.org/doc/280089},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Shamoyan, Romi F.
AU - Mihić, Olivera R.
TI - On some new sharp embedding theorems in minimal and pseudoconvex domains
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 527
EP - 546
AB - 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.
LA - eng
KW - embedding theorem; minimal domain; pseudoconvex domain; Bergman-type space; Blaschke-type infinite canonical products; area Nevanlinna-type spaces; Nevanlinna characteristic; parametric representations; zero sets
UR - http://eudml.org/doc/280089
ER -

References

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