Carleson Measures in Hardy and Weighted Bergman Spaces of Polydiscs

Jafari, F.

doi:10.2307/2048700

Cited by 3 publications

(9 citation statements)

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“…This is because theorems A and B, which are used in the proof of this theorem, are proved by using strong (p,p) type inequalities for maximal functions. [3] Proof. This theorem follows from an application of theorems A and B.…”

Section: Resultsmentioning

confidence: 99%

“…Theorems A and B , given below, make this notion precise. In [3] we discuss these spaces and measures in detail, and give various characterization and comparison theorems. These theorems which extend theorems of 'similar' type in the disc or the unit ball of C 1 to polydiscs form the foundation on which this paper is based.…”

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“…These theorems which extend theorems of 'similar' type in the disc or the unit ball of C 1 to polydiscs form the foundation on which this paper is based. For the sake of readability and to make this paper self-contained we shall state the main results of reference [3] here without proof. THEOREM A.…”

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“…We point out that condition 1 < p arises in the proofs of theorems A and B, given in [3], because of use of strong (p,p) type inequalities for maximal functions in their proof. We do not know if these theorems are also true for/?…”

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On Bounded and Compact Composition Operators in Polydiscs

Jafari

1990

Can. j. math.

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Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of Cn. Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study composition operators in poly discs and characterize those operators which are bounded or compact in Hardy and weighted Bergman spaces. In addition to Carleson measure theorems resembling those of [5], [6], we give necessary and sufficient conditions satisfied by the maps inducing bounded or compact composition operators. We conclude by considering the role of angular derivatives on the compactness question explicitly.

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On Bounded and Compact Composition Operators in Polydiscs

Jafari

1990

Can. j. math.

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“…For completeness, we give a characterization of Carleson measures for weighted Bergman space of Π + × Π + in the next section. For a characterization of Carleson measures on the bi-disc, the reader can consult [11] for unweighted Bergman spaces and [12] for standard weighted Bergman spaces.…”

Section: Second Class Of Examples: Measures Of the Formmentioning

confidence: 99%

Some Carleson measures for the Hilbert–Hardy space of tube domains over symmetric cones

Békollè

Sehba

2018

European Journal of Mathematics

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In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the corresponding embedding operator is continuous. Restricting to the case of light cones of dimension three, we prove that by freezing one or two variables, the problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue spaces reduces to the characterization of Carleson measures for Hilbert-Bergman spaces of the upper-half plane or the product of two upper-half planes.2010 Mathematics Subject Classification. Primary 32A35; 32A36; 42B25; Secondary 32A50, 32M15.

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