Some Carleson measures for the Hilbert-Hardy space of tube domains over\n symmetric cones

2017/10/30 by David Békollè, Békollé, David, Benoît F. Sehba +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1710.11237

openalex publication_date 2017/10/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this note, we obtain a full characterization of radial Carleson measures\nfor the Hilbert-Hardy space on tube domains over symmetric cones. For large\nderivatives, we also obtain a full characterization of the measures for which\nthe corresponding embedding operator is continuous. Restricting to the case of\nlight cones of dimension three, we prove that by freezing one or two variables,\nthe problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue\nspaces reduces to the characterization of Carleson measures for Hilbert-Bergman\nspaces of the upper-half plane or the product of two upper-half planes.\n

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