Pointwise multipliers and corona type decomposition in $BMOA$

Ortega, J. M.; Fàbrega, Joan

doi:10.5802/aif.1509

Cited by 109 publications

(63 citation statements)

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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%

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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“…Formulas for explicit solutions of such division problems were studied by many authors in various situations and norms (see [1], [2], [3], [4], [5], [11], [12], [14], [15], [16], [17], [18]). In particular, the H p -corona problem asks for the condition on holomorphic n-tuples G = ( …”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

DIVISION PROBLEM IN GENERALIZED GROWTH SPACES ON THE UNIT BALL IN ℂⁿ

Cho¹,

Lee²,

Park³

2015

East Asian mathematical journal

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“…A characterization of the pointwise multipliers M(Q s (D)) was obtained in [18] proving a conjecture stated in [28]. See [10,17,22,25,27,35] for more results on pointwise multipliers of function spaces.…”

Section: Introductionmentioning

confidence: 85%

“…We are going to study these spaces, and we will see that if f is in the Hardy space H p , then f ∈ Q r (T)) for 1 < p 1 , p 2 < ∞ and 0 < s, r < 1. It is worth mentioning that Stegenga [24] characterized the multipliers of bounded mean oscillation spaces on the unit circle (see also [17]), and Brown and Shields [5] described the pointwise multipliers of the Bloch space. A characterization of the pointwise multipliers M(Q s (D)) was obtained in [18] proving a conjecture stated in [28].…”

Section: Introductionmentioning

confidence: 99%

Boundary multipliers of a family of Möbius invariant function spaces

Bao¹,

Pau

2016

Ann. Acad. Sci. Fenn. Math.

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Abstract. For 1 < p < ∞ and 0 < s < 1, we consider the function spaces Q p s (T) that appear naturally as the space of boundary values of a certain family of analytic Möbius invariant function spaces on the the unit disk. In this paper, we give a complete description of the pointwise multipliers going from Q p1 s (T) to Q p2 r (T) for all ranges of 1 < p 1 , p 2 < ∞ and 0 < s, r < 1. The spectra of such multiplication operators is also obtained.

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Pointwise multipliers and corona type decomposition in $BMOA$

Cited by 109 publications

References 1 publication

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

DIVISION PROBLEM IN GENERALIZED GROWTH SPACES ON THE UNIT BALL IN ℂⁿ

Boundary multipliers of a family of Möbius invariant function spaces

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Pointwise multipliers and corona type decomposition in $BMOA$

Cited by 109 publications

References 1 publication

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

DIVISION PROBLEM IN GENERALIZED GROWTH SPACES ON THE UNIT BALL IN ℂn

Boundary multipliers of a family of Möbius invariant function spaces

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DIVISION PROBLEM IN GENERALIZED GROWTH SPACES ON THE UNIT BALL IN ℂⁿ