On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications

Krantz, Steven G.; Li, Song-Ying

doi:10.1007/s00041-001-4023-6

Cited by 39 publications

(28 citation statements)

References 14 publications

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“…We refer for example to a series of papers of Krantz and coauthors (see [9][10][11] in particular) and also [12][13][14][15] in this direction. For some new interesting results on analytic spaces in tubular domains over symmetric cones we refer the reader to [16][17][18][19] and various references there also.…”

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confidence: 99%

“…Similarly based on definition of one domain case we can define mixed norm Hardy classes on products of tubular and bounded strongly pseudoconvex domains as subspaces of In case of bounded stongly pseudocnvex domains with smooth boundary the sphere S in our defintion must be simply replaced by special ∂Ω ε domains closely related with so-called defining r function of pseudoconvex D or Ω domains to be more precise it is a set of those points of domain for which our defining function r is constant (see for standard analytic Hardy classes in bounded pseudoconvex domains with smooth boundary, for example, [9][10][11]15]). …”

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confidence: 99%

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

Shamoyan¹,

Куриленко²,

Шамоян³

et al. 2016

J. Sib. Fed. Univ., Math. phys.

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DOI: 10.17516/1997DOI: 10.17516/ -1397DOI: 10.17516/ -2016 In this note we give new estimates for traces of new mixed norm Hardy type spaces in tubular domains over symmetric cones and in bounded strictly pseudoconvex domains. We generalize a well-known one dimensional result concerning traces of Hardy spaces obtained previously in the unit disk by various authors. 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]. A rather long history related with these type estimates of traces of Hardy spaces can be read in [4] and in [2] also. In this paper we extend a known crucial estimate related with this problem to more general and complicated cases of tubular domains over symmetric cones and pseudoconvex domains with smooth boundary putting a natural condition on Bergman kernel of these domains. This paper can be considered also as continuation of a long series of papers of first author on traces of function spaces (see, for example, [5][6][7][8] and various references there).In recent decades many papers appeared where various Hardy and other analytic spaces were studied from various points of views in higher dimension in various domains in C n . We refer for example to a series of papers of Krantz and coauthors (see [9][10][11] in particular) and also [12][13][14][15] in this direction. For some new interesting results on analytic spaces in tubular domains over symmetric cones we refer the reader to [16][17][18][19] and various references there also. We will heavily use nice techniques which was developed in these papers related with so-called lattices.We start hoverer with a result in the unit ball. 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 all cases proofs actually are the same. *

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confidence: 99%

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

Shamoyan¹,

Куриленко²,

Шамоян³

et al. 2016

J. Sib. Fed. Univ., Math. phys.

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“…Let X = ∂ . We denote by d the usual quasimetric on ∂ defined in [STE1,FEF,KRL2]. (In general, the quasi-metric defined on ∂ is not symmetric, but we can defined x y = 1/2 d x y + d y x .…”

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Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, II

Krantz

2001

Journal of Mathematical Analysis and Applications

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104

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“…One can find more information on Bloch spaces in [10][11][12][13][14], etc. and their references therein.…”

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confidence: 99%

On characterizations of isometries on function spaces

Ruan

2008

Sci. China Ser. A-Math.

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On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications

Abstract: Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in C n and on domains of finite type in C 2 . Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.

Cited by 39 publications

References 14 publications

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

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

Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, II

On characterizations of isometries on function spaces

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