Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball

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Dogan O. F., ÜREYEN A. E.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.69, no.2, pp.503-523, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.21136/cmj.2018.0422-17
  • Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.503-523
  • Keywords: harmonic Bergman-Besov space, weighted harmonic Bloch space, Carleson measure, Berezin transform
  • Anadolu University Affiliated: Yes

Abstract

We consider harmonic Bergman-Besov spaces bp and weighted Bloch spaces b on the unit ball of (n) for the full ranges of parameters 0 < p < , , and determine the precise inclusion relations among them. To verify these relations we use Carleson measures and suitable radial differential operators. For harmonic Bergman spaces various characterizations of Carleson measures are known. For weighted Bloch spaces we provide a characterization when > 0.