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Random Carleson sequences for the Hardy space on the polydisc and the unit ball.

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Title: Random Carleson sequences for the Hardy space on the polydisc and the unit ball.
Authors: Chalmoukis, Nikolaos1 (AUTHOR) nikolaos.chalmoukis@unimib.it, Dayan, Alberto1,2 (AUTHOR) dayan@math.uni-sb.de, Lamberti, Giuseppe3 (AUTHOR) giuseppe.lamberti@math.u-bordeaux.fr
Source: Journal of Functional Analysis. Dec2024, Vol. 287 Issue 12, pN.PAG-N.PAG. 1p.
Subjects: Hardy spaces, Unit ball (Mathematics), Random matrices, Sequence spaces, Geometry
Abstract: We study the Kolmogorov 0 − 1 law for a random sequence with prescribed radii so that it generates a Carleson measure almost surely, both for the Hardy space on the polydisc and the Hardy space on the unit ball, thus providing improved versions of previous results of the first two authors and of a separate result of Massaneda. In the polydisc, the geometry of such sequences is not well understood, so we proceed by studying the random Gramians generated by random sequences, using tools from the theory of random matrices. Another result we prove, and that is of its own relevance, is the 0 − 1 law for a random sequence to be partitioned into M separated sequences with respect to the pseudo-hyperbolic distance, which is used also to describe the random sequences that are interpolating for the Bloch space on the unit disc almost surely. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Random Carleson sequences for the Hardy space on the polydisc and the unit ball.
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  Data: <searchLink fieldCode="AR" term="%22Chalmoukis%2C+Nikolaos%22">Chalmoukis, Nikolaos</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nikolaos.chalmoukis@unimib.it</i><br /><searchLink fieldCode="AR" term="%22Dayan%2C+Alberto%22">Dayan, Alberto</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> dayan@math.uni-sb.de</i><br /><searchLink fieldCode="AR" term="%22Lamberti%2C+Giuseppe%22">Lamberti, Giuseppe</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> giuseppe.lamberti@math.u-bordeaux.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Dec2024, Vol. 287 Issue 12, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Hardy+spaces%22">Hardy spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Unit+ball+%28Mathematics%29%22">Unit ball (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Random+matrices%22">Random matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Sequence+spaces%22">Sequence spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink>
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  Label: Abstract
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  Data: We study the Kolmogorov 0 − 1 law for a random sequence with prescribed radii so that it generates a Carleson measure almost surely, both for the Hardy space on the polydisc and the Hardy space on the unit ball, thus providing improved versions of previous results of the first two authors and of a separate result of Massaneda. In the polydisc, the geometry of such sequences is not well understood, so we proceed by studying the random Gramians generated by random sequences, using tools from the theory of random matrices. Another result we prove, and that is of its own relevance, is the 0 − 1 law for a random sequence to be partitioned into M separated sequences with respect to the pseudo-hyperbolic distance, which is used also to describe the random sequences that are interpolating for the Bloch space on the unit disc almost surely. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jfa.2024.110659
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      – Code: eng
        Text: English
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        StartPage: N.PAG
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      – SubjectFull: Hardy spaces
        Type: general
      – SubjectFull: Unit ball (Mathematics)
        Type: general
      – SubjectFull: Random matrices
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      – SubjectFull: Sequence spaces
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      – SubjectFull: Geometry
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      – TitleFull: Random Carleson sequences for the Hardy space on the polydisc and the unit ball.
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              Text: Dec2024
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              Y: 2024
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